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-   -   Status of Wagstaff testing? and testing Mersenne primes for Wagstaff-ness (https://www.mersenneforum.org/showthread.php?t=23523)

 paulunderwood 2018-11-07 16:32

[QUOTE=axn;499813][CODE]ECM found a factor in curve #14, stage #1
Sigma=3937044388854715, B1=250000, B2=25000000.
2^31601+1 has a factor: 495086555885477107 (ECM curve 14, B1=250000, B2=25000000)
Cofactor is a probable prime![/CODE]

So, (2^31601+1)/3 = 495086555885477107 · PRP9495[/QUOTE]

Congrats :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^31601+1)/3/495086555885477107" | ../../coding/gwnum/hybrid - 1 2 31601 1

Testing (x + 2)^(n + 1) == 7 (mod n, x^2 - x + 1)...
Likely prime!

real 0m1.267s
user 0m1.684s
sys 0m0.016s

[/CODE]

 axn 2018-11-10 04:35

Another one bites the dust...

[CODE]ECM found a factor in curve #211, stage #1
Sigma=7792377356163294, B1=250000, B2=25000000.
2^32377+1 has a factor: 1096170423492101317447441 (ECM curve 211, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
So, (2^32377+1)/3 = 1295081 · 568345859 · 1096170423492101317447441 · PRP9708

 paulunderwood 2018-11-10 08:01

[QUOTE=axn;500008][CODE]ECM found a factor in curve #211, stage #1
Sigma=7792377356163294, B1=250000, B2=25000000.
2^32377+1 has a factor: 1096170423492101317447441 (ECM curve 211, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
So, (2^32377+1)/3 = 1295081 · 568345859 · 1096170423492101317447441 · PRP9708[/QUOTE]

Congrats again! :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^32377+1)/3/1295081/568345859/1096170423492101317447441" | ../../coding/gwnum/hybrid - 1 2 32377 1

Testing (x + 1)^(n + 1) == 2 + 9 (mod n, x^2 - 9*x + 1)...
Likely prime!

real 0m1.517s
user 0m1.720s
sys 0m0.016s
[/CODE]

 GP2 2018-11-10 12:12

[QUOTE=axn;500008]So, (2^32377+1)/3 = 1295081 · 568345859 · 1096170423492101317447441 · PRP9708[/QUOTE]

Remarkably close to the (long-ago-discovered) PRP:

(2^32369+1)/3 = 975213233 · P9735

 axn 2018-11-12 15:57

31000-33000

31000-33000 range
[CODE]2^31019+1 = 36606080243
2^31033+1 = 37602780478825465675483
2^31033+1 = 5274911256999257402385523
2^31039+1 = 15107763782145257
2^31039+1 = 2696645101027739
2^31063+1 = 204659511295533506935963
2^31063+1 = 2459021172784025850457123
2^31079+1 = 1277922561229512977
2^31079+1 = 742254725505350547571
2^31091+1 = 5523841497517850569483
2^31091+1 = 8271765629721199361602481
2^31121+1 = 18850362981826478419075193
2^31147+1 = 6506780792059484986593698654281
2^31159+1 = 119724070256997970081
2^31159+1 = 2802563561650167604097
2^31177+1 = 11213724158959716019
2^31181+1 = 40712330002777
2^31183+1 = 118503930982958697195644551123
2^31189+1 = 14238768043105024609
2^31193+1 = 255360621097
2^31193+1 = 42530990255995354572275041
2^31249+1 = 3719124991924565051
2^31267+1 = 110134308433177831201728491
2^31277+1 = 1025970948126409451020341307147
2^31327+1 = 218594321552031025485547414177
2^31333+1 = 6202479086153575618763728459
2^31337+1 = 365015928519211619228377688833
2^31379+1 = 356411154331
2^31379+1 = 52055187923
2^31391+1 = 112913352265210696231797707
2^31393+1 = 17145060851398187
2^31469+1 = 1951459697067577
2^31469+1 = 3502361297421221333628210179
2^31477+1 = 60982260792796794657906737
2^31481+1 = 28830003790332534145507
2^31511+1 = 7953595075739102233084224505939
2^31517+1 = 153688062752403823286814121
2^31517+1 = 4930182170482960049089
2^31543+1 = 1254151095738854347
2^31543+1 = 15155197743355596931
2^31543+1 = 188337822998723
2^31547+1 = 1370919258238605165319987
2^31547+1 = 1550345168289696740737
2^31573+1 = 114782624849401
2^31573+1 = 1955500388575970267
2^31573+1 = 29487692827883
2^31601+1 = 495086555885477107
2^31607+1 = 12833547475243123
2^31607+1 = 39240620443957139393
2^31627+1 = 2384449060397716139
2^31627+1 = 360683229087339699433787
2^31627+1 = 99391080005849321
2^31643+1 = 44189041368587
2^31657+1 = 1036411181804874580356011
2^31663+1 = 8663244266350500480689660953
2^31667+1 = 3209528050261109988739649
2^31699+1 = 156842957861939
2^31723+1 = 23466170429308351842203
2^31751+1 = 24948086377594811
2^31751+1 = 4206392486368603
2^31751+1 = 90223260291763171
2^31793+1 = 29528886583076364977881
2^31793+1 = 56857512169093784593
2^31793+1 = 7100412843113
2^31799+1 = 201448575574994625529
2^31817+1 = 1106540888565041
2^31817+1 = 94915516548260491
2^31849+1 = 2845507044378448897
2^31849+1 = 79955342328194603
2^31859+1 = 21763215711715891169
2^31859+1 = 25673831025461903513
2^31873+1 = 12953215293009321752003
2^31873+1 = 89571808088547067
2^31883+1 = 1953905018801
2^31907+1 = 56281616712939139
2^31957+1 = 280833302371500996558064892449
2^31957+1 = 375021950276918773511587
2^31963+1 = 202701397797036043
2^31991+1 = 2655881239259
2^32003+1 = 4034839352712329827
2^32009+1 = 154246394640742170242807896769
2^32029+1 = 30707767118192557221069657001167817
2^32051+1 = 41364914183256811222073
2^32059+1 = 227222073190668569732452729
2^32063+1 = 14221872415938449083394092649
2^32063+1 = 1476869233241
2^32063+1 = 481295267241673
2^32069+1 = 16475196256117206740129
2^32069+1 = 821590968233530440302654346499
2^32083+1 = 5313686538537415615788587
2^32089+1 = 770180253105587
2^32117+1 = 8133839640314371
2^32119+1 = 15762867089524942521878987
2^32119+1 = 770964970991768011
2^32143+1 = 10538414766868369211445177836033
2^32143+1 = 488834835869874234117734912089
2^32183+1 = 22907599933109273385349761353
2^32191+1 = 115988035921
2^32213+1 = 17481288740841227103653993
2^32213+1 = 19864303198459
2^32213+1 = 7004020533793
2^32251+1 = 102461950405952709608662537
2^32251+1 = 1082887823235344810725281209
2^32251+1 = 194480155089308626159009
2^32261+1 = 20035167004943108272937
2^32261+1 = 284892291636291439273755734153
2^32261+1 = 8960922927525367027
2^32299+1 = 6859995781488417925241
2^32299+1 = 9714711196579667942789897
2^32309+1 = 528992441125194883
2^32321+1 = 110314967258090439165449
2^32321+1 = 19548881032669556933777
2^32323+1 = 112017905448174153386953
2^32323+1 = 150484261921914553
2^32323+1 = 374534983361537203
2^32377+1 = 1096170423492101317447441
2^32381+1 = 229818844077098285290822753
2^32401+1 = 12283015982652105937
2^32401+1 = 313709461855169
2^32411+1 = 8469881767870256579
2^32441+1 = 218976532166668822232441
2^32479+1 = 102594340411
2^32479+1 = 161911654654323443
2^32479+1 = 48951235249170377
2^32479+1 = 9048734097232340508716258723
2^32503+1 = 332079073645531837073
2^32537+1 = 35512508651
2^32537+1 = 515890733620403
2^32563+1 = 48211940575854669833
2^32569+1 = 2686336096486241
2^32569+1 = 536653053678857
2^32573+1 = 5967144942278589055954043
2^32579+1 = 74346629120914219
2^32603+1 = 191269307779486921
2^32603+1 = 9313536190619
2^32621+1 = 6617638808116327427
2^32621+1 = 80841164087689619866276265499329
2^32633+1 = 20704123369716131
2^32633+1 = 66291350494344440833
2^32633+1 = 83176245922043
2^32647+1 = 2490963022245480733043
2^32687+1 = 2312863724271662299
2^32707+1 = 175670507562950044616608657
2^32713+1 = 1688940684727378005212763528403
2^32717+1 = 15140183610295019483
2^32717+1 = 73712912581215203
2^32749+1 = 127806462751729929976988537
2^32749+1 = 822763844266061653642875779
2^32789+1 = 2241035428544443
2^32789+1 = 284616454939
2^32789+1 = 48393678569
2^32797+1 = 441006813487097706920689
2^32801+1 = 1774839018097
2^32803+1 = 201960985553
2^32831+1 = 48839511362107
2^32833+1 = 21586533441429999980159153
2^32839+1 = 202873512709703201
2^32843+1 = 158257194106457433569
2^32843+1 = 33700468092622182014430484249
2^32843+1 = 9096613171504318617600431761
2^32869+1 = 311191050788338180723
2^32909+1 = 4555345024778819801874439209979
2^32909+1 = 866791730633
2^32911+1 = 589105255651317323
2^32911+1 = 60251236321455100763539
2^32917+1 = 69732228612833771015441
2^32933+1 = 429789704854085417867
2^32933+1 = 8269997574955395036451
2^32939+1 = 486826270513356865653860593
2^32941+1 = 255973706353
2^32941+1 = 664335677489904571609
2^32957+1 = 747655621398500993555483
2^32971+1 = 16507553749495887019
2^32983+1 = 139967167125222523
2^32987+1 = 50238411426599440816555994129
2^32987+1 = 70054165025290522051
2^32993+1 = 141076677979829475388117601369
2^32999+1 = 2244279413473
2^32999+1 = 350995249459
2^32999+1 = 818078604261655777099[/CODE]

 GP2 2018-11-15 02:22

Mersenne primes and Wagstaff primes do not share the same exponents, beyond the very small exponents that inspired the new Mersenne conjecture: 3, 5, 7, 13, 17, 19, 31, 61, 127.

But what about exponents of fully-factored composite Mersenne numbers and exponents of fully-factored composite Wagstaff numbers? I wondered if there are any correlations and compared the two lists. Links to them can be found [URL="http://mprime.s3-website.us-west-1.amazonaws.com/mersenne/"]on this page[/URL] and [URL="http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/"]on this page[/URL].

I ignored the range under 1200, where the Cunningham project has fully factored nearly everything. Apart from those, the two lists have the following exponents in common: 1459, 7417, 8849.

We can probably ignore the first one (1459) because it is still pretty close to the Cunningham project range of very small exponents. But I was kind of surprised to see the two larger ones (7417 and 8849) because it seems like too much of a coincidence.

In the range between 7000 and 8000, there are 107 prime numbers. None of these are exponents of Mersenne primes or Wagstaff primes. Only 5 out of 107 are exponents of fully-factored Mersenne numbers and only 1 out of 107 is an exponent of a fully-factored Wagstaff number... but 7417 is a member of both subsets.

In the range between 8000 and 9000, there are 110 prime numbers. None of these are exponents of Mersenne primes or Wagstaff primes. Only 2 out of 110 are exponents of fully-factored Mersenne numbers and only 4 out of 110 are exponents of fully-factored Wagstaff numbers... but 8849 is a member of both subsets.

The largest factor of M7417 (other than the prime cofactor) is 25 digits long. The largest factor of W7417 is 33 digits long. The largest factor of M8849 is 20 digits long. The largest factor of W8849 is 30 digits long.

Obviously the set of fully-factored exponents is not statically defined, it grows slowly over time as we factor to greater depths.

And there are no coincidences in the ranges 2k, 3k, 4k, 5k, 6k, or 9k... or higher. So far, anyway, perhaps we might find some if we do deeper ECM testing (beyond t30 for Wagstaff or beyond t40 for Mersenne).

But still, what are the odds of randomly selecting 5 objects out of 107 without replacement, and then selecting 1 object out of 107, and it turns out that the intersection of the two selections is non-empty? And then repeating the exercise with 2 out of 110 and then 4 out of 110, and again end up with a non-empty intersection?

 science_man_88 2018-11-15 02:48

[QUOTE=GP2;500262]
But still, what are the odds of randomly selecting 5 objects out of 107 without replacement, and then selecting 1 object out of 107, and it turns out that the intersection of the two selections is non-empty? And then repeating the exercise with 2 out of 110 and then 4 out of 110, and again end up with a non-empty intersection?[/QUOTE]

First, it depends on if the selections of 107 are the same. If so, it's obvious 5/107 ~4.67% . The second one, I'm too lazy to work out but would suspect about 1/55

 GP2 2018-11-15 14:31

[QUOTE=science_man_88;500265]First, it depends on if the selections of 107 are the same. If so, it's obvious 5/107 ~4.67% . The second one, I'm too lazy to work out but would suspect about 1/55[/QUOTE]

Yeah, I don't mean astronomical odds, I just mean "makes you go hmmm" odds. And not just one, but the two cases occurring together.

There are 988 not-fully-factored exponents of Wagstaff numbers in the 0 to 10000 range. I'm going to run ECM on them to t=40, trying to create more fully-factored exponents. I'll start slowly and then throw more resources at it if anything turns up in the 2k or 3k ranges.

 GP2 2018-11-15 14:33

In a possibly related vein, there's a few people doing fairly deep factorization of Wagstaff numbers with Mersenne-prime exponents and then PRP testing the cofactors.

So far there are no PRPs. [URL="http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html"]The page is here[/URL].

 axn 2018-11-15 15:38

[QUOTE=GP2;500283]
There are 988 not-fully-factored exponents of Wagstaff numbers in the 0 to 10000 range. I'm going to run ECM on them to t=40, trying to create more fully-factored exponents. I'll start slowly and then throw more resources at it if anything turns up in the 2k or 3k ranges.[/QUOTE]

Right now I'm running t35 on these (started at 1300, currently at around 2800). t40 would probably have more success. But it would probably be better to work your way down from 10500, rather than up from 1300. It does look like t40 or similar has been already run on the lower ones, so odds of success will be low there. But if you're starting from 1300 onwards, I'll stop my t35 run (after it reaches 3000).

 GP2 2018-11-15 16:09

[QUOTE=axn;500290]Right now I'm running t35 on these (started at 1300, currently at around 2800). t40 would probably have more success. But it would probably be better to work your way down from 10500, rather than up from 1300. It does look like t40 or similar has been already run on the lower ones, so odds of success will be low there. But if you're starting from 1300 onwards, I'll stop my t35 run (after it reaches 3000).[/QUOTE]

OK, I only started a couple of hours ago, so I switched to doing t35, working downward from 10,000. I guess we can coordinate at some point about meeting in the middle.

I am omitting the exponents 2203, 2281, 3217, 4253, 4423, 9689, 9941, which have already been deeply ECM'd by the [URL="http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html"]Mersenneplustwo project[/URL] I mentioned a couple of messages ago.

(And 1279 is already fully-factored. When I mentioned that there aren't any Wagstaff PRPs for Mersenne-prime exponents, obviously I wasn't including the very small exponents.)

Have you found any new factors so far?

 axn 2018-11-15 16:58

[QUOTE=GP2;500293]Have you found any new factors so far?[/QUOTE]
Just the two from post 192. Which, btw, was totally unexpected -- I would've expected all p40s and smaller to have been found already, for such small exponents. I wouldn't expect anymore success from t35 for a while - hopefully, working backwards would be more productive.

 GP2 2018-11-16 17:41

[QUOTE=axn;500290]It does look like t40 or similar has been already run on the lower ones, so odds of success will be low there.[/QUOTE]

Here are the current counts of known factors of size 35 digits or more in each range:

[CODE]
1k 46
2k 31
3k 3
4k 5
5k 1
6k 8
7k 5
8k 3
9k 5
[/CODE]

So yes, there definitely was more done in the 1k and 2k ranges. But even in the higher ranges I wonder if it wasn't done to t=35 already.

There are roughly 110 to 120 prime exponents in each range, with the 1k and 2k ranges at around 130.

 axn 2018-11-17 04:14

[QUOTE=GP2;500360]So yes, there definitely was more done in the 1k and 2k ranges. But even in the higher ranges I wonder if it wasn't done to t=35 already.[/QUOTE]
It is likely that some sporadic t35 or higher was run on the 3k-10k ranges, so there maybe some that were left out. Even if a systematic t35 has been run already, another round of t35 will find some more factors. A full t40 will be about 8-9x as costly as a t35, so that is a substantial investment of time.

Perhaps we could switch places. You can take 3k onwards to t40 (using P95 + GMP-ECM - just P95 alone would not be most efficient). I can work my way downwards from 10k to t35. What do you think?

 DukeBG 2018-11-17 09:21

Factors of the 33000-34000 range were added to FactorDB by someone.

 axn 2018-11-17 09:55

[QUOTE=DukeBG;500387]Factors of the 33000-34000 range were added to FactorDB by someone.[/QUOTE]

I am doing t30 on 33000-35000 range. Currently around 34300...

 GP2 2018-11-17 13:57

[QUOTE=axn;500380]Perhaps we could switch places. You can take 3k onwards to t40 (using P95 + GMP-ECM - just P95 alone would not be most efficient). I can work my way downwards from 10k to t35. What do you think?[/QUOTE]

OK, let's do that.

I already did the following exponents before stopping:

[CODE]
UID: GP2/c5.large, 2^9887+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 0657232B
UID: GP2/c5.large, 2^9907+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 0663232F
UID: GP2/c5.large, 2^9923+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 0642232E
UID: GP2/c5.large, 2^9929+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 06482323
UID: GP2/c5.large, 2^9931+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 064A2325
UID: GP2/c5.large, 2^9949+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 06642326
UID: GP2/c5.large, 2^9967+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 06402327
UID: GP2/c5.large, 2^9973+1 completed 1580 ECM curves, B1=1000000, B2=100000000, Wg8: 064E232D
[/CODE]

I didn't get around to doing 9901, and I skipped 9941 because it's a Mersenne prime exponent and the Mersenneplustwo project has already ECM'd it to t=50+

 GP2 2018-11-18 13:50

Hmmm, maybe it's not surprising that Mersenne numbers and Wagstaff numbers with the same exponent may be correlated in terms of being fully-factored.

After all if M[SUB]p[/SUB] = 2[SUP]p[/SUP] − 1 and W[SUB]p[/SUB] = (2[SUP]p[/SUP] + 1) /3, then:

3 * M[SUB]p[/SUB] * W[SUB]p[/SUB] = M[SUB]2p[/SUB]

and, as [URL="http://www.primenumbers.net/Documents/TestNP.pdf"]the Lifchitz duo pointed out[/URL]:

2 * M[SUB]p[/SUB] * W[SUB]p[/SUB] = W[SUB]2p+1[/SUB] − 1

I imagine the factors of any random composite number N are distributed unpredictably between 2 and sqrt(N), and there is always at least a small probability that it will end up having only small prime factors plus a huge cofactor that splits into exactly two prime factors of roughly equal size. So if M[SUB]14834[/SUB] and M[SUB]17698[/SUB] satisfy that condition, as they do, then both M[SUB]7417[/SUB], W[SUB]7417[/SUB] and both M[SUB]8849[/SUB], W[SUB]8849[/SUB] will be fully factored if we are lucky and the two huge prime cofactors get split up and go separately into each of the two components.

PS,

It might be worthwhile to go trawling through FactorDB, to see if anyone has reported factors for Mersenne numbers whose exponents are 2 times a prime, to see if there are any undiscovered Wagstaff factors sitting there in plain sight...

 GP2 2018-11-18 14:19

The Lifchitz duo, in their paper, point out that by the equation in the previous message, if either M[SUB]p[/SUB] or W[SUB]p[/SUB] is prime, and p is a Sophie Germain prime (i.e., 2p+1 is also prime), then if W[SUB]2p+1[/SUB] happens to be a probable prime also, then it should be straightforward to certify that it is prime by the N−1 method.

Actually, I think that M[SUB]p[/SUB] or W[SUB]p[/SUB] don't have to be prime, one of them just needs to be fully-factored.

Of course the catch is, it is really extremely unlikely that W[SUB]2p+1[/SUB] will just happen to be prime, for anything but very small p.

The Lifchitzes, writing in the year 2000, discuss the exponents 5, 7, 11, 23, 47, 179, 383, 7079, 19379, 21383, 43403, 166679 and 1718867, none of which are exponents of Wagstaff primes. From Mersenne primes and Wagstaff primes discovered since then, we can add: W[SUB]8,062,799[/SUB] (has a factor), W[SUB]26,694,623[/SUB] (no factor to 75 bits, but PRP tested as composite), and W[SUB]86,225,219[/SUB] (no factor to 75 bits, I'm PRP testing it now, but what are the odds?). And the currently known fully-factored Mersenne numbers and fully-factored Wagstaff numbers don't yield any Sophie Germain p for which the safe prime 2p+1 is larger than 1M, and everything is already tested composite.

We could also work backward: W[SUB]83339[/SUB] is a Wagstaff prime, which was very laboriously certified prime by ECPP. But 83339 is a safe prime corresponding to the Sophie Germain prime 41669, so if by some extremely unlikely sheer luck we managed to fully factor either M[SUB]41669[/SUB] or W[SUB]41669[/SUB], then we would have an alternative easy N−1 proof. The safe-prime exponents of known Wagstaff primes, along with their Sophie-Germain prime counterparts are:
[CODE]
3 7
5 11
11 23
83 167
173 347
2903 5807
5639 11279
41669 83339
[/CODE]

and unfortunately nothing bigger.

This approach is also really extremely unlikely to be fruitful. There aren't any undiscovered Wagstaff primes smaller than 5M, and probably not smaller than 10M, and even if we found one, its exponent would need to be a safe prime, and then we would have to hope that the Mersenne number or Wagstaff number with the Sophie-Germain-prime counterpart exponent of size 2M or 3M or higher would somehow miraculously get fully factored at some point in the future.

 GP2 2018-11-18 16:26

[QUOTE=GP2;500443]...if we are lucky and the two huge prime cofactors get split up and go separately into each of the two components.[/QUOTE]

But of course they have to go separately into each of the two components, because M[SUB]p[/SUB] and W[SUB]p[/SUB] are necessarily of nearly comparable size...

 DukeBG 2018-11-18 18:20

[QUOTE=GP2;500443]It might be worthwhile to go trawling through FactorDB, to see if anyone has reported factors for Mersenne numbers whose exponents are 2 times a prime, to see if there are any undiscovered Wagstaff factors sitting there in plain sight...[/QUOTE]

I did that before, there's none.

 science_man_88 2018-11-18 18:42

[QUOTE=DukeBG;500458]I did that before, there's none.[/QUOTE]

2^(2p)-1== (2^p+1)(2^p-1) so they'd show up as mersennes with prime exponents and factors of 2^p+1

 GP2 2018-11-18 20:39

[QUOTE=GP2;500445]The Lifchitzes, writing in the year 2000, discuss the exponents 5, 7, 11, 23, 47, 179, 383, 7079, 19379, 21383, 43403, 166679 and 1718867, none of which are exponents of Wagstaff primes.[/QUOTE]

Except the first four obviously are...

 GP2 2018-11-20 07:24

We can look for the same phenomenon in other bases.

The generalized repunits are:

R[SUP]b[/SUP][SUB]p[/SUB] = (b[SUP]p[/SUP] − 1) / (b − 1)

which also implies that for negative b and odd p:

R[SUP]−b[/SUP][SUB]p[/SUB] = (b[SUP]p[/SUP] + 1) / (b + 1)

Note for the base b=2 we have the special cases of Mersenne and Wagstaff numbers.

For bases other than b=2, ECM factoring beyond the Cunningham exponent range has been done only in limited cases and to at most t=25, which limits the number of known fully-factored exponents.

Still, if we ignore anything below 1500, we find the following:

In the range between 2000 and 3000, there are 127 prime numbers.
For R[SUP]3[/SUP] we have nine known fully-factored exponents, and for R[SUP]−3[/SUP] we have four known fully-factored exponents, and 2131 is a member of both subsets.

In the range between 3000 and 4000, there are 120 prime numbers.
For R[SUP]5[/SUP] we have one known fully-factored exponent, and for R[SUP]−5[/SUP] we have one known fully-factored exponent, and it is one and the same: 3203.

No coincidences turn up for b=6 and b=7. Well, actually for b=6 we have p=1187, 1409, but these are below the threshold of 1500 that we set. Although perhaps we should still count them, because the larger b is, the less thoroughly the Cunningham project has fully factored the smallish exponents.

For b higher than 7 the FactorDB data is too patchy at the moment.

 axn 2018-11-21 15:26

33000-35000

33000-35000 range
[CODE]2^33013+1 = 244323344600583960643
2^33029+1 = 45013308419
2^33073+1 = 17222305654955729
2^33091+1 = 124387312463539
2^33091+1 = 1581153397174269019
2^33091+1 = 436504452972184865713
2^33119+1 = 538702194827
2^33149+1 = 13237626462989728832803
2^33179+1 = 7354499400278955028073223211115971
2^33191+1 = 1335895311662383504024122457
2^33203+1 = 16097743599829179275664540179
2^33203+1 = 718854557547996076657401257
2^33211+1 = 170860276964275609
2^33211+1 = 7544093761366633
2^33211+1 = 7861460408778833
2^33223+1 = 126848177122404791539
2^33223+1 = 132916318483299713
2^33287+1 = 152116186738774997580371281
2^33287+1 = 2501062389726383774449
2^33289+1 = 12177540892142364314419
2^33289+1 = 183263610982401590323
2^33301+1 = 3549171768274817491922009
2^33301+1 = 952657805611851281
2^33317+1 = 115645840757851
2^33329+1 = 278243447158508283011569
2^33331+1 = 480185938164587
2^33331+1 = 620715582909909563057
2^33331+1 = 687762221807537
2^33347+1 = 1313921489529582668553131
2^33347+1 = 2699773920329
2^33347+1 = 732531534190517329441
2^33349+1 = 149656459113403767580619
2^33353+1 = 30385004648627
2^33409+1 = 4366631937977
2^33413+1 = 532725306062509138128599028257
2^33461+1 = 10014073565014892632177
2^33461+1 = 11981740945115171
2^33469+1 = 46434139988636941006153
2^33479+1 = 1494930625639988954497
2^33479+1 = 7225229942369
2^33487+1 = 135909003481851401
2^33493+1 = 13033009992785363083
2^33493+1 = 815884670636813130108656273
2^33503+1 = 1199487539177
2^33503+1 = 6521458587923
2^33529+1 = 34713085274259031420343723
2^33533+1 = 299422108770288128041
2^33533+1 = 408893428013472489073756907
2^33533+1 = 55789230203611589136220651
2^33533+1 = 7026547473977
2^33547+1 = 3682958195311464985691
2^33569+1 = 268438297101930031971113
2^33569+1 = 33598703521929131
2^33599+1 = 187056272196467429888449
2^33599+1 = 416719592976080321
2^33601+1 = 10910027959271456657
2^33601+1 = 15015193010076399729289979
2^33617+1 = 40637329384323590916196033
2^33629+1 = 1409418420107437042823545969
2^33721+1 = 1295616014293988215211
2^33767+1 = 8323998309620918477707841
2^33773+1 = 161986565290660601
2^33791+1 = 160721309767457
2^33791+1 = 32496687310067
2^33797+1 = 1938529204723
2^33797+1 = 2181904765676237701033868562427
2^33811+1 = 884809052200294129553
2^33827+1 = 209133637849008818963
2^33829+1 = 10035523992138395983481
2^33829+1 = 45606465061170283
2^33863+1 = 432857771928520441
2^33871+1 = 31686284597364513499
2^33889+1 = 115840810661192689459
2^33923+1 = 17260283622599554393
2^33923+1 = 375667847683
2^33937+1 = 5659022510467
2^33961+1 = 2720840357008876913
2^33997+1 = 578864124358664515699
2^34019+1 = 2945883469561
2^34019+1 = 331516200084153691395331667
2^34019+1 = 43933412621320527423429871969
2^34031+1 = 12844836650455262153
2^34033+1 = 108065182512001907
2^34039+1 = 1136707956349891472467
2^34127+1 = 931760715845870405095416329
2^34129+1 = 47871798425320095068719633
2^34141+1 = 2532499149913186204819
2^34147+1 = 41982431853138060908971
2^34171+1 = 155553263856443
2^34213+1 = 62409807693419
2^34231+1 = 2534471762672809681
2^34231+1 = 3305136413977
2^34273+1 = 22727428553793770588053923659
2^34273+1 = 8451030376499
2^34283+1 = 357857836034034043330540923659
2^34301+1 = 6533573278339673804301803
2^34313+1 = 585292729634651
2^34337+1 = 20141353814137937177
2^34337+1 = 27396950810066451227
2^34351+1 = 257790997496422384340443024307209
2^34351+1 = 3934104151916747
2^34351+1 = 44685813781616550941898002539
2^34367+1 = 1012393079369295206873
2^34381+1 = 293668051321891
2^34403+1 = 4936507954231490257
2^34421+1 = 8790590859694832953
2^34457+1 = 48003597884253796365227
2^34469+1 = 183864725557362813883
2^34483+1 = 6216908137845443
2^34511+1 = 17878376212788825883
2^34519+1 = 105543750039055740998969
2^34519+1 = 1408511576725511386626622907
2^34549+1 = 60544939716289365976914816442378681
2^34603+1 = 27322193561083963
2^34607+1 = 1053855121693403
2^34631+1 = 428731898803616108946230238859
2^34651+1 = 88964571347
2^34667+1 = 173923437659
2^34673+1 = 174284181073707501049250873
2^34679+1 = 1000251912481739780354291
2^34679+1 = 34735850317579337
2^34703+1 = 1608699418926762499
2^34721+1 = 42355547062053019
2^34729+1 = 7651793557960376720347
2^34739+1 = 18083223457113209
2^34739+1 = 974826623738688955873
2^34757+1 = 159322816744035432052633
2^34759+1 = 2409451067999054935915970896873
2^34759+1 = 804946991825430611
2^34763+1 = 15248664848634989793427326491
2^34763+1 = 769982993756138555925509113
2^34763+1 = 84324862363998441139
2^34781+1 = 131145081991829433611899
2^34781+1 = 1392522504123119576347193201
2^34807+1 = 3308781771917867467
2^34819+1 = 18321677781314441466419
2^34819+1 = 297408428301239363
2^34847+1 = 3388958014193603857
2^34849+1 = 1175071822091369
2^34849+1 = 357955745877569111177203
2^34849+1 = 6074351530191475465991292233
2^34877+1 = 3004977184910519678088994003
2^34877+1 = 61207936396321988201
2^34877+1 = 858534082772688708473
2^34877+1 = 97229778311829176968771
2^34919+1 = 3948913813971410593
[/CODE]

 pinhodecarlos 2018-11-21 19:38

25500-26000

[CODE]
2^25561+1 has a factor: 136909595564491867571 (ECM curve 23, B1=250000, B2=25000000)
2^25561+1 has a factor: 136909595564491867571 (ECM curve 3, B1=250000, B2=25000000)
2^25561+1 has a factor: 136909595564491867571 (ECM curve 74, B1=250000, B2=25000000)
2^25583+1 has a factor: 2108375531451544092169 (ECM curve 4, B1=250000, B2=25000000)
2^25589+1 has a factor: 4533217425232723910897 (ECM curve 55, B1=250000, B2=25000000)
2^25609+1 has a factor: 4267185478594256099199502969 (ECM curve 143, B1=250000, B2=25000000)
2^25621+1 has a factor: 368252059833694969 (ECM curve 4, B1=250000, B2=25000000)
2^25639+1 has a factor: 2703117300877515230230787 (ECM curve 85, B1=250000, B2=25000000)
2^25657+1 has a factor: 42188428063252774609 (ECM curve 9, B1=250000, B2=25000000)
2^25673+1 has a factor: 2460099335748156782199019 (ECM curve 49, B1=250000, B2=25000000)
2^25733+1 has a factor: 239001603528530737936039699 (ECM curve 274, B1=250000, B2=25000000)
2^25747+1 has a factor: 869465213607265690470233 (ECM curve 38, B1=250000, B2=25000000)
2^25801+1 has a factor: 683773135900148971 (ECM curve 3, B1=250000, B2=25000000)
2^25841+1 has a factor: 410369752966734745420949220543683 (ECM curve 180, B1=250000, B2=25000000)
2^25847+1 has a factor: 12680442819865294557718499 (ECM curve 255, B1=250000, B2=25000000)
2^25847+1 has a factor: 46751657557521312289475607363658939 (ECM curve 299, B1=250000, B2=25000000)
2^25903+1 has a factor: 15016808139977443 (ECM curve 5, B1=250000, B2=25000000)
2^25919+1 has a factor: 5922210067999919923 (ECM curve 2, B1=250000, B2=25000000)
2^25931+1 has a factor: 1891570224656668841936972723 (ECM curve 109, B1=250000, B2=25000000)
2^25951+1 has a factor: 23260238273143196107 (ECM curve 134, B1=250000, B2=25000000)
2^25951+1 has a factor: 23260238273143196107 (ECM curve 5, B1=250000, B2=25000000)
2^25951+1 has a factor: 317907539894705471225293187 (ECM curve 108, B1=250000, B2=25000000)

[/CODE]

26000-26500 still testing..

 axn 2018-11-23 13:19

... and another one

[CODE]ECM found a factor in curve #10, stage #2
Sigma=7210635612416542, B1=250000, B2=25000000.
2^35677+1 has a factor: 1174478776290172030409 (ECM curve 10, B1=250000, B2=25000000)
ECM found a factor in curve #38, stage #2
Sigma=1699163987306510, B1=250000, B2=25000000.
2^35677+1 has a factor: 4519369329719894060013787 (ECM curve 38, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus (2^35677+1)/3 = 1174478776290172030409 · 4519369329719894060013787 · PRP10694

 paulunderwood 2018-11-23 14:49

[QUOTE=axn;500831][CODE]ECM found a factor in curve #10, stage #2
Sigma=7210635612416542, B1=250000, B2=25000000.
2^35677+1 has a factor: 1174478776290172030409 (ECM curve 10, B1=250000, B2=25000000)
ECM found a factor in curve #38, stage #2
Sigma=1699163987306510, B1=250000, B2=25000000.
2^35677+1 has a factor: 4519369329719894060013787 (ECM curve 38, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus (2^35677+1)/3 = 1174478776290172030409 · 4519369329719894060013787 · PRP10694[/QUOTE]

Congrats :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^35677+1)/3/1174478776290172030409/4519369329719894060013787" | ../../coding/gwnum/hybrid - 1 2 35677 1

Testing (x + 2)^(n + 1) == 7 (mod n, x^2 - x + 1)...
Likely prime!

real 0m1.115s
user 0m0.900s
sys 0m0.036s
[/CODE]

 axn 2018-11-23 16:30

... and another one

[CODE]ECM found a factor in curve #2, stage #1
Sigma=461605036619020, B1=250000, B2=25000000.
2^35851+1 has a factor: 54919454473787 (ECM curve 2, B1=250000, B2=25000000)
ECM found a factor in curve #111, stage #2
Sigma=2529484593925455, B1=250000, B2=25000000.
2^35851+1 has a factor: 1383891629171890065880777 (ECM curve 111, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
(2^35851+1)/3 = 1184732147 · 54919454473787 · 1383891629171890065880777 · PRP10745

 paulunderwood 2018-11-23 17:19

[QUOTE=axn;500843][CODE]ECM found a factor in curve #2, stage #1
Sigma=461605036619020, B1=250000, B2=25000000.
2^35851+1 has a factor: 54919454473787 (ECM curve 2, B1=250000, B2=25000000)
ECM found a factor in curve #111, stage #2
Sigma=2529484593925455, B1=250000, B2=25000000.
2^35851+1 has a factor: 1383891629171890065880777 (ECM curve 111, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
(2^35851+1)/3 = 1184732147 · 54919454473787 · 1383891629171890065880777 · PRP10745[/QUOTE]

Congrats again :toot: :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^35851+1)/3/1184732147/54919454473787/1383891629171890065880777" | ../../coding/gwnum/hybrid - 1 2 35851 1

Testing (x + 2)^(n + 1) == 5 (mod n, x^2 + 1)...
Likely prime!

real 0m0.703s
user 0m0.888s
sys 0m0.008s
[/CODE]

 axn 2018-11-24 08:19

[QUOTE=axn;497976]
[CODE]ECM found a factor in curve #1, stage #2
Sigma=7791075725288429, B1=250000, B2=25000000.
2^29027+1 has a factor: 275322488297 (ECM curve 1, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus (2^29027+1)/3 = 578914489 · 275322488297 · PRP8718[/QUOTE]

[QUOTE=axn;498055][CODE]ECM found a factor in curve #390, stage #2
Sigma=7844702814691327, B1=250000, B2=25000000.
2^29437+1 has a factor: 24192412837755888627020059 (ECM curve 390, B1=250000, B2=25000000)
Cofactor is a probable prime![/CODE]

(2^29437+1)/3 = 1177481 · 24192412837755888627020059 · PRP8830[/QUOTE]
These two are now proven (long time back... waiting for factordb to upload it)

 pinhodecarlos 2018-11-26 19:40

26000-26500 done

[CODE]
2^26017+1 has a factor: 628295109713251741345216912537379 (ECM curve 399, B1=250000, B2=25000000)
2^26021+1 has a factor: 20056522540355505315086219 (ECM curve 45, B1=250000, B2=25000000)
2^26041+1 has a factor: 131880107821847253060288953 (ECM curve 137, B1=250000, B2=25000000)
2^26041+1 has a factor: 5133597786411701095883 (ECM curve 3, B1=250000, B2=25000000)
2^26053+1 has a factor: 185255101747907703065087656691 (ECM curve 77, B1=250000, B2=25000000)
2^26053+1 has a factor: 4197165704910243992819 (ECM curve 101, B1=250000, B2=25000000)
2^26083+1 has a factor: 1118283355318735860011 (ECM curve 18, B1=250000, B2=25000000)
2^26083+1 has a factor: 55421847303778673 (ECM curve 2, B1=250000, B2=25000000)
2^26107+1 has a factor: 859528261417318515403 (ECM curve 44, B1=250000, B2=25000000)
2^26107+1 has a factor: 859528261417318515403 (ECM curve 6, B1=250000, B2=25000000)
2^26119+1 has a factor: 33599180088532561 (ECM curve 110, B1=250000, B2=25000000)
2^26119+1 has a factor: 33599180088532561 (ECM curve 6, B1=250000, B2=25000000)
2^26119+1 has a factor: 4069121945248193970904063489 (ECM curve 55, B1=250000, B2=25000000)
2^26119+1 has a factor: 4069121945248193970904063489 (ECM curve 77, B1=250000, B2=25000000)
2^26141+1 has a factor: 12302651387100233 (ECM curve 3, B1=250000, B2=25000000)
2^26177+1 has a factor: 2209568257662624159233 (ECM curve 110, B1=250000, B2=25000000)
2^26177+1 has a factor: 6699363221022123855592841 (ECM curve 139, B1=250000, B2=25000000)
2^26183+1 has a factor: 6326277643729527361793969 (ECM curve 137, B1=250000, B2=25000000)
2^26189+1 has a factor: 21939023541432339273131 (ECM curve 76, B1=250000, B2=25000000)
2^26237+1 has a factor: 4940480327570136992401935019 (ECM curve 184, B1=250000, B2=25000000)
2^26249+1 has a factor: 61769675275297363243 (ECM curve 62, B1=250000, B2=25000000)
2^26263+1 has a factor: 27775488948006877565753 (ECM curve 70, B1=250000, B2=25000000)
2^26293+1 has a factor: 5178618228283053971 (ECM curve 15, B1=250000, B2=25000000)
2^26297+1 has a factor: 331056202075107398295261259 (ECM curve 28, B1=250000, B2=25000000)
2^26297+1 has a factor: 336250445903171 (ECM curve 2, B1=250000, B2=25000000)
2^26321+1 has a factor: 45467342717607470637587 (ECM curve 2, B1=250000, B2=25000000)
2^26393+1 has a factor: 182532853384830323 (ECM curve 2, B1=250000, B2=25000000)
2^26399+1 has a factor: 2527029406443001360675782573227 (ECM curve 515, B1=250000, B2=25000000)
2^26399+1 has a factor: 7913514683358829152208219 (ECM curve 3, B1=250000, B2=25000000)
2^26417+1 has a factor: 62150979840284417056493607362041 (ECM curve 231, B1=250000, B2=25000000)
2^26423+1 has a factor: 872930940764728645666579 (ECM curve 7, B1=250000, B2=25000000)
2^26431+1 has a factor: 4775290088417746293443 (ECM curve 7, B1=250000, B2=25000000)
2^26437+1 has a factor: 1287872173435586759323 (ECM curve 155, B1=250000, B2=25000000)
2^26437+1 has a factor: 1287872173435586759323 (ECM curve 98, B1=250000, B2=25000000)
2^26479+1 has a factor: 1504735026754535267 (ECM curve 18, B1=250000, B2=25000000)
2^26479+1 has a factor: 1504735026754535267 (ECM curve 287, B1=250000, B2=25000000)
2^26489+1 has a factor: 31055541621204479789435950003 (ECM curve 378, B1=250000, B2=25000000)
2^26489+1 has a factor: 5601166359596957819 (ECM curve 6, B1=250000, B2=25000000)
2^26497+1 has a factor: 442348719449699348137687049 (ECM curve 424, B1=250000, B2=25000000)

[/CODE]

 axn 2018-11-28 16:17

35000-37000. Not all of it is reported to factordb.
[CODE]2^35023+1 = 113183376254043141161
2^35059+1 = 122100260976161936953
2^35059+1 = 5081250871604071390846834931
2^35081+1 = 42152949521270544720121
2^35083+1 = 46237943078921329470331
2^35099+1 = 1330412517631594162811
2^35107+1 = 9928924318289607289
2^35111+1 = 332188260769
2^35111+1 = 5020413836529499
2^35111+1 = 84114660640714864610704172014550771
2^35117+1 = 224034332481330219209
2^35117+1 = 370749342883
2^35129+1 = 40671179984315413051
2^35141+1 = 193910602584159151907
2^35149+1 = 1570482697579
2^35149+1 = 5552794488958059617
2^35149+1 = 94748900554963
2^35159+1 = 170014297293457
2^35221+1 = 212128656885735673
2^35221+1 = 2310054119427673
2^35221+1 = 77348454012545842284065592464509187
2^35227+1 = 522224860125658870711323721
2^35251+1 = 531468250524618163
2^35251+1 = 65905552225620396770969
2^35257+1 = 84237223139
2^35281+1 = 23561017638982590006455257074049
2^35281+1 = 2388708612307531
2^35281+1 = 723905516838433
2^35291+1 = 366926718925073711771
2^35311+1 = 20311032643556721673
2^35317+1 = 185952660922694115011
2^35317+1 = 57941635273
2^35317+1 = 7595806110725113
2^35317+1 = 808832383226407913382001
2^35317+1 = 924413349087665689963
2^35323+1 = 1158266403574290489148692787
2^35327+1 = 15861087845131
2^35327+1 = 339986992508954715068221152957883
2^35419+1 = 7123371688953535409899575162977
2^35423+1 = 120634278827563257315011
2^35437+1 = 1326826778122120195928088619
2^35447+1 = 166594150747018714502197187
2^35447+1 = 1829477324478848226067
2^35461+1 = 599811705298988911307
2^35509+1 = 330303349230688544092512209
2^35531+1 = 410890099257097
2^35533+1 = 286781794840618937
2^35573+1 = 198875338699
2^35573+1 = 76965173633
2^35591+1 = 59278826015269387547
2^35617+1 = 83719614027791626580103817
2^35671+1 = 3676508930160410422569353
2^35677+1 = 1174478776290172030409
2^35677+1 = 4519369329719894060013787
2^35729+1 = 11221428467401
2^35731+1 = 301454157409
2^35747+1 = 424807296153399643459
2^35753+1 = 9833561824259
2^35759+1 = 285651750017440388794327184819
2^35759+1 = 573620060003
2^35771+1 = 538309462516863571
2^35801+1 = 536982295291368094245580771510325003
2^35809+1 = 2039488914148187993
2^35831+1 = 10176242338242543169
2^35831+1 = 1056205199655132118582241
2^35831+1 = 1676614447177907
2^35837+1 = 17607815123702487186134209
2^35837+1 = 214243621506777271889947
2^35837+1 = 7053251225616658999496547429053194571
2^35851+1 = 1383891629171890065880777
2^35851+1 = 54919454473787
2^35869+1 = 9932173231867
2^35879+1 = 58508597140221097
2^35897+1 = 23665958656417027977414033521
2^35897+1 = 390126898730394569
2^35923+1 = 252955049935486907
2^35933+1 = 238587570463524141962563
2^35951+1 = 14154366526626523289
2^35951+1 = 457540284625947517811298761
2^35951+1 = 63641949967735689569
2^35963+1 = 32096378846064876121
2^35969+1 = 123351271295739759349144777
2^35969+1 = 679299672584947
2^35993+1 = 7409860505483353
2^35993+1 = 8529379072805540266448233
2^36011+1 = 325036680207277651
2^36011+1 = 34271946340058389293421577
2^36013+1 = 19836518047817753795657
2^36017+1 = 134275137380776133473249012507
2^36061+1 = 1228607914303348144264240427
2^36061+1 = 621725967557322227
2^36067+1 = 1439002616132767805892453953
2^36067+1 = 165532812644249
2^36073+1 = 150085079624224771457
2^36097+1 = 576403976273941124833
2^36107+1 = 93109339819051849
2^36131+1 = 516273598430455433
2^36131+1 = 70043565369613924747
2^36137+1 = 104062202277266472233
2^36151+1 = 158695587499
2^36161+1 = 164299973820272891
2^36209+1 = 22515145857367084547
2^36217+1 = 7112551120199282411
2^36229+1 = 1233776075773010201
2^36251+1 = 2536244699859780305881
2^36319+1 = 63907929223829294904575617
2^36341+1 = 1890670883762627
2^36341+1 = 25866531152475940335125831531
2^36341+1 = 4074672053346216578613068819
2^36373+1 = 308756722823171502965753
2^36389+1 = 10913417212344757619
2^36389+1 = 840498081116297
2^36433+1 = 5163870767108471777
2^36433+1 = 538347196747
2^36451+1 = 105553581258909331
2^36451+1 = 8279212954171
2^36457+1 = 21422791117896457
2^36467+1 = 3426110538122843
2^36473+1 = 232877752734045451
2^36473+1 = 39553477578619901169307219
2^36479+1 = 1656256823245894937
2^36479+1 = 33870616158305418891131
2^36551+1 = 64240001943585886102793
2^36559+1 = 10906743102656195102467
2^36571+1 = 1546411998474267593
2^36583+1 = 2407209361035002089
2^36599+1 = 335141857392877792552800320115523
2^36607+1 = 56109203446684836103966333390273
2^36629+1 = 374881991273
2^36629+1 = 86147123433826617641
2^36653+1 = 92624194046918357608861382805992497
2^36677+1 = 155494995915451821014690881
2^36683+1 = 297225455443920180251
2^36683+1 = 56429825731
2^36691+1 = 113599597854846121
2^36691+1 = 147611335469240199560209
2^36709+1 = 3563439321965963771
2^36713+1 = 21895318418062336952051
2^36713+1 = 63051090132131
2^36713+1 = 94130434511908956913
2^36739+1 = 13302000107046451
2^36761+1 = 27802425541811
2^36779+1 = 10694783157446139957212312283007241
2^36781+1 = 3107786068546457
2^36791+1 = 1697152292227030627081
2^36791+1 = 320299932830262659
2^36809+1 = 160239957139
2^36809+1 = 2895485669441367276097393
2^36821+1 = 3784645085803
2^36821+1 = 91194520656277173482107
2^36833+1 = 361414478796803
2^36833+1 = 9010185614956079339
2^36847+1 = 11989062800607888058633
2^36847+1 = 17455251492458150529131
2^36847+1 = 3973327193723
2^36857+1 = 6077049154912019783593585687283
2^36887+1 = 33899737186976594086855201
2^36899+1 = 10130794613281
2^36899+1 = 12632969385867659
2^36901+1 = 37891440257273
2^36913+1 = 196321550950142097643
2^36931+1 = 752337650641
2^36931+1 = 964926802350402223417
2^36943+1 = 44208867677630448846065611
2^36943+1 = 613936728299
2^36979+1 = 80640886583732873
2^36997+1 = 105202897796309030699[/CODE]

 DukeBG 2018-12-13 18:04

Factors that I've found added in FDB (from about last week), most likely from GP2's t40:

[URL="http://factordb.com/index.php?id=1100000000017315340"]2^3089+1[/URL]: P35+C879
[URL="http://factordb.com/index.php?id=1100000000017315425"]2^3109+1[/URL]: P35+P36+P44+C807 (nice!)
[URL="http://factordb.com/index.php?id=1100000000017315642"]2^3167+1[/URL]: P35+C890

Looks like t40 is going fairly well!

 GP2 2018-12-13 20:06

[QUOTE=DukeBG;502644]Factors that I've found added in FDB (from about last week), most likely from GP2's t40:[/QUOTE]

Yes, that was me. However, I will probably pause the t40 ECM soon because spot prices in the cloud are starting to rise, as they usually do at this time of year. Presumably for online holiday shopping, and maybe also corporations and accounting firms doing some quarter-end and year-end financial crunching.

 GP2 2018-12-13 23:19

(2^1430131+1)/(3*356468732537*36519993971459) is a 430487-digit PRP

Some background:

The factoring efforts from 2013 stopped when a first factor was found, because they were mainly interested in just eliminating potential Wagstaff primes. So there are a lot of second-and-higher factors still waiting to be found, some of them actually quite small.

I redid the range from 1M to 2M and found more than 16,000 new factors. One of them resulted in the above PRP. I'm going on work on ranges below 1M next.

So the Gerbicz cofactor-compositeness test was really useful once again, because I did the original PRP test on (2^1430131+1)/3 (with no divisors) several months ago. The new cofactors were checked very quickly, in an afternoon on a single core, whereas redoing all the PRP tests would have taken very much longer.

 paulunderwood 2018-12-13 23:54

[QUOTE=GP2;502686](2^1430131+1)/(3*356468732537*36519993971459) is a 430487-digit PRP

Some background:

The factoring efforts from 2013 stopped when a first factor was found, because they were mainly interested in just eliminating potential Wagstaff primes. So there are a lot of second-and-higher factors still waiting to be found, some of them actually quite small.

I redid the range from 1M to 2M and found more than 16,000 new factors. One of them resulted in the above PRP. I'm going on work on ranges below 1M next.

So the Gerbicz cofactor-compositeness test was really useful once again, because I did the original PRP test on (2^1430131+1)/3 (with no divisors) several months ago. The new cofactors were checked very quickly, in an afternoon on a single core, whereas redoing all the PRP tests would have taken very much longer.[/QUOTE]

Congrats to you for the find and to Robert for his method in action,

[CODE]time ./pfgw64 -k -f0 -od -q"(2^1430131+1)/(3*356468732537*36519993971459)" | ../../coding/gwnum/hybrid - 1 2 1430131 1

Testing (x + 1)^(n + 1) == 2 + 5 (mod n, x^2 - 5*x + 1)...
Likely prime!

real 20m31.553s
user 43m12.772s
sys 4m21.160s
[/CODE]

 GP2 2018-12-14 02:42

[QUOTE=GP2;502686](2^1430131+1)/(3*356468732537*36519993971459) is a 430487-digit PRP

I'm going on work on ranges below 1M next.[/QUOTE]

Tesla V100 is really fast. :smile:

In the range from 500k to 1M there were 8541 new second-and-higher factors of size 56 bits or less, and two new PRPs:

(2^730339+1)/(3*27839062003*7943469324347)
(2^758231+1)/(3*27146942976539*73236839266867)

In the 1M to 2M range earlier, I found 16143 new second-and-higher factors of size 57 bits or less, plus the PRP cofactor of exponent 1430131.

 axn 2018-12-14 02:52

[QUOTE=GP2;502702]Tesla V100 is really fast. :smile:

In the range from 500k to 1M there were 8541 new second-and-higher factors of size 56 bits or less, and two new PRPs:

(2^730339+1)/(3*27839062003*7943469324347)
(2^758231+1)/(3*27146942976539*73236839266867)[/QUOTE]

:tu:

 paulunderwood 2018-12-14 03:39

[QUOTE=GP2;502702]Tesla V100 is really fast. :smile:

In the range from 500k to 1M there were 8541 new second-and-higher factors of size 56 bits or less, and two new PRPs:

(2^730339+1)/(3*27839062003*7943469324347)
(2^758231+1)/(3*27146942976539*73236839266867)

In the 1M to 2M range earlier, I found 16143 new second-and-higher factors of size 57 bits or less, plus the PRP cofactor of exponent 1430131.[/QUOTE]

Congrats again :toot: :toot:

[CODE] time ./pfgw64 -k -f0 -od -q"(2^730339+1)/(3*27839062003*7943469324347)" | ../../coding/gwnum/hybrid - 1 2 730339 1

Testing (x + 2)^(n + 1) == 5 (mod n, x^2 + 1)...
Likely prime!

real 5m39.409s
user 11m12.568s
sys 3m39.148s
[/CODE]

[CODE]time ./pfgw64 -k -f0 -od -q"(2^758231+1)/(3*27146942976539*73236839266867)" | ../../coding/gwnum/hybrid - 1 2 758231 1

Testing (x + 2)^(n + 1) == 5 (mod n, x^2 + 1)...
Likely prime!

real 6m8.764s
user 11m49.092s
sys 4m2.044s
[/CODE]

 GP2 2018-12-15 04:13

Found one more PRP in the space between 200k and 500k:

(2^318271+1)/(3*46031404238891*654090604244843)

 paulunderwood 2018-12-15 05:18

[QUOTE=GP2;502848]Found one more PRP in the space between 200k and 500k:

(2^318271+1)/(3*46031404238891*654090604244843)[/QUOTE]

Congrats! :smile:

[CODE]time ../../Maths_misc/pfgw/pfgw64 -k -f0 -od -q"(2^318271+1)/(3*46031404238891*654090604244843)" | ../../coding/gwnum/hybrid - 1 2 318271 1

Testing (x + 2)^(n + 1) == 5 (mod n, x^2 + 1)...
Likely prime!

real 1m17.354s
user 2m19.836s
sys 0m54.920s
[/CODE]

 axn 2018-12-21 17:47

37000-40000. This includes known factors in some subranges, because factordb was down while i was preparing the worktodo
[CODE]2^37003+1 = 1420915201
2^37003+1 = 33193957153818718077193
2^37013+1 = 2052375661691
2^37013+1 = 74027
2^37019+1 = 1872582788308966931
2^37019+1 = 28805732125660364618237572867
2^37019+1 = 331062557784977938363
2^37021+1 = 198544733042446002571
2^37049+1 = 170549069563
2^37049+1 = 19046848812337
2^37049+1 = 348706369424206469039371067
2^37061+1 = 1055571403
2^37087+1 = 507221520780316559930265131
2^37097+1 = 120726102593
2^37097+1 = 29158243
2^37117+1 = 3395885477227
2^37139+1 = 2323341563
2^37139+1 = 297113
2^37139+1 = 39388834196251
2^37159+1 = 63681905113
2^37171+1 = 24653089448304419637708571
2^37171+1 = 63896768485290351153073
2^37181+1 = 10352480539710847619
2^37181+1 = 230094333076717255902219511561
2^37181+1 = 3014527271002125673
2^37181+1 = 33015272335964251
2^37181+1 = 563098982615796024731
2^37181+1 = 68710489
2^37189+1 = 227650994088233
2^37189+1 = 246471636131631089089
2^37189+1 = 6094676712751177
2^37201+1 = 155190459014481128705180851
2^37217+1 = 1010339798723
2^37217+1 = 97803131332010077125881
2^37223+1 = 48590531108112962739763
2^37243+1 = 8691195750924721
2^37253+1 = 17285393
2^37253+1 = 5667794205889
2^37253+1 = 96957318381543769
2^37277+1 = 334887800719897018081
2^37307+1 = 223843
2^37307+1 = 829356390050443
2^37309+1 = 157966307
2^37309+1 = 373091
2^37313+1 = 15432656801
2^37313+1 = 602076553280598114577946851
2^37321+1 = 671779
2^37339+1 = 212085521
2^37339+1 = 866563513
2^37357+1 = 214878942960892878685187
2^37357+1 = 76208281
2^37361+1 = 2622527023355489
2^37369+1 = 1511249919050742107
2^37369+1 = 43055105181790921
2^37379+1 = 11737943740793960009
2^37379+1 = 150338339
2^37409+1 = 777807929
2^37423+1 = 817346162713
2^37423+1 = 898153
2^37441+1 = 10306649234215300180365063693731
2^37441+1 = 17672153
2^37447+1 = 224683
2^37447+1 = 84405539
2^37463+1 = 14961584749547166488455613243
2^37463+1 = 6276925651
2^37483+1 = 132130504058380646799662741747
2^37483+1 = 240420502287535968461801713081
2^37489+1 = 108396140344211
2^37489+1 = 174906363754163
2^37489+1 = 391160227
2^37489+1 = 87733463637678258830434201
2^37493+1 = 11924011465563293355697771
2^37493+1 = 132463777228200632538304283
2^37501+1 = 130035482854788306044535027602748487346872118419
2^37501+1 = 158722904893698011798881
2^37501+1 = 5403387905503869889303939
2^37501+1 = 68470121495255575057819249
2^37501+1 = 842696194514699290975843057
2^37501+1 = 975912598643
2^37507+1 = 5968359510851
2^37507+1 = 866489939603
2^37511+1 = 271279553
2^37511+1 = 3445300950251
2^37511+1 = 99680092919521
2^37517+1 = 25179708028609
2^37517+1 = 3249030201283
2^37529+1 = 300233
2^37529+1 = 983051597472245251337
2^37537+1 = 5698412464766177080197327401
2^37537+1 = 7376034013321
2^37549+1 = 4414147325818737479412958657677232873
2^37549+1 = 7719916994593
2^37561+1 = 42449349989402527939
2^37561+1 = 96565827802417000276211
2^37567+1 = 1127011
2^37571+1 = 47414603
2^37573+1 = 23026873567304265868108313
2^37573+1 = 759167513679659730503747
2^37589+1 = 513206311051066361305769
2^37591+1 = 7620766287811429449343649
2^37591+1 = 832309849201
2^37591+1 = 9156164972849
2^37607+1 = 316714836323779
2^37619+1 = 158502013651
2^37619+1 = 192106036718938959518363603
2^37643+1 = 225859
2^37643+1 = 56668755435161
2^37649+1 = 677683
2^37657+1 = 14549211541057
2^37657+1 = 19902446974323307
2^37663+1 = 1033792163798569658809
2^37663+1 = 8843639312947
2^37691+1 = 22117782015703236293422913
2^37691+1 = 8026599979
2^37691+1 = 92368504499
2^37699+1 = 1228384217
2^37699+1 = 5353259
2^37717+1 = 377171
2^37717+1 = 601162354546337
2^37717+1 = 695309291366953
2^37717+1 = 93743677735247659040177
2^37747+1 = 226483
2^37781+1 = 131114845368468979
2^37783+1 = 55320537957544806664467279281
2^37799+1 = 325190987105742613672777
2^37799+1 = 6350233
2^37811+1 = 13883584536740052619
2^37811+1 = 1551691850574613995620329739
2^37811+1 = 2284169988630511177453680088796699
2^37831+1 = 1165086341473819
2^37831+1 = 16013137554265384387763
2^37831+1 = 444928359131424608483
2^37847+1 = 2119433
2^37853+1 = 109912479696841
2^37861+1 = 2430709685782841
2^37861+1 = 37165796107658591217569
2^37871+1 = 190237976850129643019411
2^37871+1 = 32717817289
2^37879+1 = 1371518592405349313
2^37879+1 = 2802031373107
2^37879+1 = 30019984171577
2^37879+1 = 4930519656211
2^37897+1 = 682147
2^37907+1 = 49190549249
2^37907+1 = 6009017386765470689
2^37951+1 = 13056276761449
2^37951+1 = 1317326693076769
2^37951+1 = 8186015386063774192091
2^37957+1 = 120957149286763
2^37963+1 = 1515717222915587
2^37963+1 = 207200167420957512693282641
2^37963+1 = 560003697812988019
2^37963+1 = 8527649239583615926533875749930147
2^37987+1 = 73100055529
2^37991+1 = 42009156107
2^38039+1 = 22225065689787833
2^38047+1 = 15528863002579257978683
2^38047+1 = 33785737
2^38053+1 = 123955284865337
2^38053+1 = 1600175643996580723
2^38053+1 = 2435393
2^38053+1 = 301879833074047672441
2^38069+1 = 90339369030546348814056691
2^38113+1 = 1257265435862630275009
2^38149+1 = 293364462272129
2^38149+1 = 69042441691
2^38149+1 = 871309956757413140853569
2^38177+1 = 293944683395936296211
2^38183+1 = 120972495771623301283
2^38197+1 = 14153959765259759681950627
2^38197+1 = 44294301627577286490982793
2^38197+1 = 465331543814998801
2^38231+1 = 194224184681
2^38231+1 = 59084808624968317266871985107
2^38237+1 = 3432434945455801913
2^38239+1 = 1010694443904059
2^38239+1 = 108472371365958740924524089121236809
2^38239+1 = 276838249299912394134320419
2^38261+1 = 178977271697655505883
2^38273+1 = 299893842589540431107
2^38329+1 = 331784261904358771
2^38333+1 = 2190206422887043718911825146637207947779
2^38333+1 = 6643059220433
2^38351+1 = 1073113155384971
2^38351+1 = 230387036129
2^38351+1 = 71852985475492646766900884837507
2^38371+1 = 17271997398083
2^38371+1 = 58664597775950137
2^38393+1 = 4974117431200206353908053307
2^38393+1 = 6933895087939334477739374039644648668705169
2^38447+1 = 1307962711628697979
2^38459+1 = 161378075344019
2^38459+1 = 3358023995095499
2^38459+1 = 99478827103391188283
2^38561+1 = 2264959044825251842657
2^38569+1 = 19954053842361023676388860017
2^38609+1 = 1369832689310592348481
2^38609+1 = 22930582560916601582233
2^38639+1 = 429008545743567293051719953209
2^38653+1 = 11511391852683937
2^38653+1 = 8339644517950337
2^38671+1 = 37356201411021439699
2^38677+1 = 98358024252111187
2^38693+1 = 9738664074893814405953089
2^38699+1 = 712666806404072499953
2^38707+1 = 6676772786369580809
2^38713+1 = 1007409979309383217
2^38713+1 = 569188694874152576973499
2^38737+1 = 237235469761209058807325683513
2^38747+1 = 306437070575347
2^38747+1 = 881358684476209
2^38767+1 = 725696189283910536067
2^38783+1 = 1049264921655764128177
2^38783+1 = 59017099459
2^38803+1 = 1322424591646264819
2^38833+1 = 36006526120705816387
2^38833+1 = 49445959103737810297
2^38861+1 = 108869264917382555737
2^38861+1 = 554826693692148907
2^38867+1 = 26952010129634667929
2^38873+1 = 3544282919006707
2^38891+1 = 58175957953
2^38903+1 = 525239042921546074296641
2^38917+1 = 730993732365428344579738280707
2^38917+1 = 73874195251
2^38923+1 = 5312442896146702709777
2^38953+1 = 2737426902073211576596721
2^38953+1 = 8701573010099
2^38959+1 = 70606272683212768771946273
2^38959+1 = 989354614347556858123
2^38977+1 = 18855453651329
2^39041+1 = 32793190614847824895739
2^39043+1 = 35890104987155973353
2^39089+1 = 125366675985433272825348289
2^39089+1 = 17325242429459
2^39089+1 = 9632637851329
2^39103+1 = 125753312557913
2^39113+1 = 11118156267917015180706812377
2^39113+1 = 77572884529436099
2^39133+1 = 33661520989841
2^39157+1 = 1171866060686707
2^39157+1 = 4283480472311082411683197853467
2^39163+1 = 72772174950222878336356961
2^39181+1 = 53577039921949479639091
2^39181+1 = 68742519178843
2^39191+1 = 848530783117327879811099954011
2^39217+1 = 1042424260924079754163
2^39229+1 = 2728855915835596553
2^39229+1 = 336077276845619
2^39239+1 = 5099340562622782939
2^39251+1 = 142363553425961664826049
2^39301+1 = 127083792203
2^39301+1 = 357696862066077353277433
2^39301+1 = 6260903355204405049403
2^39313+1 = 20374424633723342598828163
2^39323+1 = 197913374032052099107
2^39341+1 = 4909124119832972467
2^39367+1 = 83586846304513
2^39371+1 = 18136326520776863257
2^39373+1 = 421024243744043
2^39383+1 = 1529481112612456273
2^39383+1 = 6889168405518722123
2^39397+1 = 13311537522511028249
2^39397+1 = 13585692897838927844612947
2^39409+1 = 18641433406605707
2^39439+1 = 668058931844258257
2^39443+1 = 263646741089267
2^39443+1 = 2864408211477568369
2^39461+1 = 2721188686754199931
2^39499+1 = 4037288625491361291973169
2^39541+1 = 657930388587933497
2^39551+1 = 18562150308697
2^39551+1 = 34181980543129
2^39563+1 = 204951840059973635058105331
2^39569+1 = 32871179427953
2^39623+1 = 62125911660495220468127420921
2^39631+1 = 412637954800147
2^39659+1 = 1228311172201016179
2^39667+1 = 1003316203870172995992179603
2^39679+1 = 967460613430018259
2^39703+1 = 4647241470203
2^39719+1 = 251181858462003482249401177
2^39733+1 = 3017196325448873
2^39769+1 = 56486345111691419849
2^39799+1 = 74642469542708917261099
2^39829+1 = 2754896958917667733618193
2^39839+1 = 80924721667
2^39839+1 = 87303104923
2^39847+1 = 306214753119464081
2^39869+1 = 46883784455747
2^39869+1 = 57588709092878450611
2^39877+1 = 156745328243354125673401
2^39901+1 = 12051726620807312209
2^39901+1 = 18557064408251659
2^39929+1 = 900538224364298299249
2^39953+1 = 288317496043137571
2^39979+1 = 600607489967979135350963
[/CODE]

 axn 2018-12-22 13:06

40k-42k done to t25
[CODE]2^40031+1 = 6825843174948850751129
2^40037+1 = 1995121642147039741091
2^40063+1 = 11674067422747
2^40063+1 = 63725810321
2^40111+1 = 314419308428273999964329
2^40111+1 = 490437008374332289
2^40177+1 = 847770616389859
2^40189+1 = 74828395182071418367313
2^40189+1 = 765332382508692787
2^40213+1 = 21523465037827640580078913
2^40253+1 = 48015791051
2^40277+1 = 402395474387168992643
2^40283+1 = 366118019587493153
2^40289+1 = 10113952338121
2^40289+1 = 943821051590034481
2^40343+1 = 37176165755867
2^40343+1 = 43577332771028683793
2^40351+1 = 789053537258097401866633
2^40387+1 = 374924164561475827120313
2^40493+1 = 531013407113963654267
2^40519+1 = 5899550538590036299086233
2^40543+1 = 24889524219023414369
2^40543+1 = 8024349314858587
2^40559+1 = 4728386649279539
2^40577+1 = 504447134955878688347
2^40591+1 = 3179034432883
2^40699+1 = 471799196899606441
2^40751+1 = 2491624073156348649611
2^40759+1 = 418945480661650409
2^40763+1 = 24446052218291703426759641
2^40771+1 = 52684144529488525484965169
2^40787+1 = 209460593970292154034386531
2^40819+1 = 2361989536177186273
2^40819+1 = 5479471203526229197726441
2^40823+1 = 111465650227
2^40841+1 = 216150391320481
2^40841+1 = 56860473841
2^40883+1 = 1176804799830337
2^40883+1 = 26936308311822979041198091
2^40897+1 = 102133305011
2^40897+1 = 577663336099
2^40903+1 = 794600290027299649
2^40927+1 = 1201582898292268841
2^40949+1 = 1657418360980836623521393
2^40949+1 = 45336136254376057
2^40961+1 = 177015111801678265085353
2^40961+1 = 251116040248850277833
2^40961+1 = 2896977538130307525059
2^40961+1 = 34165829055443
2^41011+1 = 108259523448390255233
2^41017+1 = 117054536552653886561
2^41023+1 = 230017618985569
2^41039+1 = 77091140102697318361
2^41113+1 = 472114163792135306329
2^41131+1 = 43491163905793
2^41131+1 = 870626128913
2^41143+1 = 528746713301648738579
2^41149+1 = 59308642390432489
2^41189+1 = 111551097787
2^41189+1 = 328493555596187
2^41201+1 = 995088443863492437589747
2^41203+1 = 111055517179
2^41221+1 = 149714898798860511714137
2^41221+1 = 35289106625093460509243
2^41221+1 = 830695403917073
2^41227+1 = 78090608219266810411
2^41231+1 = 49199855379846235891
2^41243+1 = 654092574553057
2^41263+1 = 431332870268411
2^41333+1 = 996702898478432857
2^41341+1 = 1574567570470633139706401
2^41341+1 = 18813331422577811769043
2^41357+1 = 20690616057984225953
2^41357+1 = 368180321342972304208961
2^41389+1 = 1273621435789736281
2^41389+1 = 5509947219644674283
2^41413+1 = 1187373409283
2^41453+1 = 257347865319812279107
2^41453+1 = 397652125190113
2^41491+1 = 349957057682912633491
2^41507+1 = 12225375279462547
2^41507+1 = 2435801685827
2^41507+1 = 2591812236769106781883
2^41579+1 = 148794363103884300529
2^41593+1 = 5124515191105649
2^41603+1 = 4511480536527986709089
2^41611+1 = 10810654830105281
2^41611+1 = 66977195912893651291
2^41627+1 = 323017120097244211
2^41647+1 = 246203231466308941267
2^41651+1 = 21031740395446902497
2^41687+1 = 106806288867034206543433
2^41687+1 = 1652599061111566889
2^41719+1 = 128291089337589056881751449
2^41809+1 = 15361294684874594462464867
2^41813+1 = 419205644805002861219
2^41813+1 = 63584693905736538212691585479689
2^41849+1 = 4515519164169286444987
2^41849+1 = 6220894250707300883
2^41879+1 = 3525249084577189696635059
2^41893+1 = 87580782242955851
2^41897+1 = 174087934860681987986579
2^41897+1 = 2946080967880849
2^41897+1 = 70681156781018051
2^41897+1 = 7518521850259918481
2^41953+1 = 1863180654394006941683
2^41959+1 = 812857944449
2^41981+1 = 6228788678953752209
2^41999+1 = 50122194587[/CODE]

 GP2 2018-12-22 18:29

Re: the exponent of the new Mersenne prime:

[QUOTE=ATH;503542]Found no factors of the corresponding Wagstaff number, but it is not prime

[CODE]no factor for W82589933 from 2^78 to 2^79 [mfaktc 0.21 barrett87_mul32_gs]
(and half way to 2^80 without factors)
[/QUOTE]

I finished the TF=80 level:

[CODE]
no factor for W82589933 from 2^79 to 2^80 [mfaktc 0.21 barrett87_mul32_gs]
[/CODE]

 paulunderwood 2018-12-22 18:39

[QUOTE=GP2;503683]Re: the exponent of the new Mersenne prime:

I finished the TF=80 level:

[CODE]
no factor for W82589933 from 2^79 to 2^80 [mfaktc 0.21 barrett87_mul32_gs]
[/CODE][/QUOTE]

[quote] 2^82589933-3 has small factors: 23,40343[/quote]

Is it time to test the co-factor? Oh no, not Wagstaff :rolleyes:

 axn 2018-12-23 12:44

42k-44k to t25
[CODE]2^42017+1 = 886691699693896619
2^42019+1 = 417732519753117761
2^42023+1 = 3100602195814665237569758009
2^42061+1 = 17388552079433
2^42071+1 = 8685786832509707880078961
2^42073+1 = 55587916674931
2^42083+1 = 5619115994299
2^42083+1 = 70372761689852688789433
2^42131+1 = 9706456183811
2^42139+1 = 1349606906779
2^42169+1 = 9310841766271248653563
2^42193+1 = 3910039794186164292337
2^42197+1 = 2585026564291697489
2^42197+1 = 312629471177
2^42197+1 = 83379537053214382482193
2^42209+1 = 2736510773309097377936521
2^42209+1 = 4020000574411866494809
2^42221+1 = 503590555291
2^42221+1 = 50430338172163
2^42227+1 = 572500086846753533626387
2^42257+1 = 111396973747
2^42257+1 = 166072325686050907
2^42257+1 = 2477594507033
2^42257+1 = 4484356671288591673
2^42281+1 = 28011749886368852958593
2^42281+1 = 720904830620426376227
2^42323+1 = 1089455846369507
2^42331+1 = 449344834931
2^42349+1 = 182686699713809
2^42349+1 = 332997005527793
2^42373+1 = 2319545941953331263113
2^42391+1 = 28816636983423534577
2^42397+1 = 6967189683241509697
2^42397+1 = 9816517625495411993
2^42409+1 = 558797154441182147
2^42433+1 = 178085588930333219
2^42433+1 = 95189699557327051
2^42451+1 = 71849516830116297521443
2^42457+1 = 162231894155561
2^42461+1 = 154401189067
2^42461+1 = 26477648307233
2^42467+1 = 266266945245868532100627868819
2^42499+1 = 108202369003
2^42533+1 = 206346016802201
2^42569+1 = 458288382737861716571
2^42571+1 = 11446834368539
2^42577+1 = 1722347250059036803
2^42589+1 = 8085431098126538707
2^42643+1 = 34825939982854079467
2^42649+1 = 4629250424827283
2^42667+1 = 148898976222286403
2^42683+1 = 42951673501445087473
2^42689+1 = 40147467697
2^42701+1 = 51167410692911559751609
2^42703+1 = 78482562611
2^42709+1 = 29307389351085773367443617
2^42719+1 = 478166811903784415681
2^42719+1 = 8079920821053138227
2^42727+1 = 2293160140897
2^42727+1 = 72610809564287064842683
2^42743+1 = 8956082795780217721849
2^42767+1 = 705275985643
2^42773+1 = 28500514837316692931
2^42793+1 = 2516313594016121
2^42793+1 = 67784539931
2^42797+1 = 283975382978710979089
2^42821+1 = 559560302466362132027
2^42841+1 = 130937905201248928783977731
2^42841+1 = 6851471078219
2^42853+1 = 24556136426603877787
2^42901+1 = 38227162996291
2^42901+1 = 702310048283
2^42943+1 = 1335050612583781081
2^42961+1 = 17560798505401
2^42961+1 = 2746319320226309520224761
2^42967+1 = 208572817553
2^42967+1 = 3305515439364643
2^42967+1 = 92179170863612049627187
2^42979+1 = 240306585221616417233
2^42979+1 = 6263974698833
2^42989+1 = 769861553631097
2^43013+1 = 115574525765291
2^43019+1 = 1574589353497
2^43037+1 = 6911714765041066567291
2^43049+1 = 33213180854203739
2^43103+1 = 4472889054262801577
2^43103+1 = 7118635564766718521
2^43189+1 = 240855844219998257
2^43201+1 = 1735228028395870681
2^43201+1 = 5739491282194337
2^43201+1 = 84212625247603
2^43261+1 = 83929985431427
2^43271+1 = 10037796595861470407312801
2^43283+1 = 62188321873
2^43283+1 = 63343792165612243
2^43321+1 = 1241890692407608045690093553
2^43427+1 = 1425019967588219
2^43457+1 = 253569179787059721089
2^43457+1 = 28492742883468130523
2^43481+1 = 109031241328043626820741257
2^43487+1 = 253121771829737378753
2^43499+1 = 1198069396549633
2^43517+1 = 313603786130114561
2^43541+1 = 6999036867603030763459
2^43573+1 = 1447612423701209
2^43577+1 = 1089679093978817927281
2^43577+1 = 7593938671219
2^43591+1 = 20137272471049743923
2^43597+1 = 437554259611811
2^43649+1 = 1058631156827
2^43649+1 = 43527478326911057
2^43651+1 = 58335318669639336786353
2^43661+1 = 12314988901380936055283
2^43661+1 = 1319758144469522935571
2^43711+1 = 36410066961154943472043171241
2^43711+1 = 847794701995402516753
2^43721+1 = 207272783645245298993
2^43759+1 = 13919531199292011399419
2^43787+1 = 228151242338472290395321
2^43789+1 = 9083810944139
2^43793+1 = 948696474735660333379337
2^43801+1 = 18240904902256169857961
2^43891+1 = 2519391968575065215041
2^43891+1 = 3162068910199549035987659
2^43913+1 = 520178675288491
2^43943+1 = 1158580880218568729243
2^43951+1 = 16097989039878114641
2^43963+1 = 212923975603
2^43969+1 = 108819053977
2^43969+1 = 260841343849
2^43969+1 = 28384508275737547937473[/CODE]

 axn 2018-12-25 13:53

44k-47k to t25
[CODE]2^44017+1 = 267194752391898449
2^44021+1 = 124069137634402633
2^44027+1 = 4415740999123244966281
2^44053+1 = 83909550720192670483
2^44071+1 = 287479038209589888223633
2^44071+1 = 596623824186443
2^44087+1 = 19118504572426966659687283
2^44101+1 = 5481190502231761
2^44111+1 = 7252485474922433899
2^44131+1 = 118426799050909889809
2^44131+1 = 5892148311892711168291
2^44159+1 = 111064747249161714194531
2^44189+1 = 18445742035574175107
2^44189+1 = 75695080930251613832367194721319937
2^44203+1 = 131477189257481
2^44203+1 = 1640386491915725523499
2^44207+1 = 389819263644090121
2^44221+1 = 19984311041507290529
2^44221+1 = 5401890805486667595953
2^44221+1 = 84276876062096891
2^44249+1 = 110637293454504748196963
2^44249+1 = 226980696701269737491819
2^44263+1 = 1627249428893802281
2^44263+1 = 36723831729142530026233
2^44267+1 = 5014370044966706651
2^44269+1 = 1765909474339047091
2^44269+1 = 3181310819223614148017
2^44273+1 = 1829378918179049
2^44279+1 = 295846747978241939
2^44293+1 = 1229667755497249
2^44293+1 = 47633257748727817393
2^44351+1 = 3507907708453504670971
2^44357+1 = 184250828383225267
2^44357+1 = 4674404819617294928939
2^44381+1 = 25111697137766329116337
2^44383+1 = 35376188769756072193
2^44453+1 = 1001071676879323054859339
2^44483+1 = 7203540974573720557379
2^44491+1 = 269825106267933163104691
2^44491+1 = 301388371298041
2^44491+1 = 8355449795629361
2^44507+1 = 10238704970749486057
2^44507+1 = 2669531741845349954100547
2^44533+1 = 7143384145295464745849
2^44543+1 = 3850435181473
2^44549+1 = 61494967311829924762651
2^44587+1 = 166092835897031198033
2^44617+1 = 2831912823371
2^44633+1 = 37355937356357154937
2^44657+1 = 10652225374934391193081
2^44687+1 = 448804211429219864327849
2^44711+1 = 4036889711723549587
2^44729+1 = 828118162939
2^44741+1 = 356190006165844407847889614498003
2^44789+1 = 79036550539
2^44809+1 = 116114723105613661493627
2^44809+1 = 1900748894074374467
2^44867+1 = 376669443507389991419
2^44879+1 = 2351224300784088352700793736729
2^44879+1 = 329377576801930417
2^44893+1 = 351349228411
2^44893+1 = 579047739666383153
2^44909+1 = 1289406729497
2^44909+1 = 16925917597622827
2^44917+1 = 1337548883722189753
2^44927+1 = 25881326576214493201
2^44939+1 = 13102384958578474205461027
2^44939+1 = 18808927263630889002723816379
2^44953+1 = 209092586081
2^44971+1 = 65523036587375918713
2^44983+1 = 379944068249609
2^45007+1 = 4762445137864858862827
2^45061+1 = 22553984899221212579
2^45061+1 = 814362295020920034089
2^45121+1 = 1116499382003
2^45121+1 = 459185750485843
2^45121+1 = 512680606642027466500483529
2^45127+1 = 212566996754087203643706019
2^45127+1 = 215739502888184441099
2^45127+1 = 72312663888078049
2^45127+1 = 77059587233
2^45131+1 = 13879323856918383708851
2^45137+1 = 1794806453611
2^45137+1 = 2007104451329
2^45179+1 = 232645343590575329
2^45181+1 = 30568948181171
2^45233+1 = 512446955329590159223764473
2^45247+1 = 311406381352867249
2^45263+1 = 513217241281
2^45263+1 = 62918702373097268752938217
2^45281+1 = 332427944279944273
2^45289+1 = 305679464171
2^45289+1 = 580370901825454103459
2^45307+1 = 157821610049833365379
2^45319+1 = 162268820334284574815229467
2^45319+1 = 355767926977
2^45319+1 = 657986332139051
2^45329+1 = 140786071889
2^45361+1 = 52612409831086142973491
2^45377+1 = 280212289990561
2^45389+1 = 685549008898729352651
2^45413+1 = 107834905981796824489
2^45433+1 = 332393651420209
2^45481+1 = 10930049309399699
2^45497+1 = 3015781325533313576316817
2^45503+1 = 16960822484760067
2^45541+1 = 109164672672139537027
2^45541+1 = 930149786369
2^45569+1 = 196106837577283
2^45569+1 = 757695659885886451
2^45587+1 = 24723899383690771123290251
2^45589+1 = 110293229057723507
2^45613+1 = 77198266153082285603842027
2^45641+1 = 1162317358854677328155161
2^45659+1 = 2579070292844728273691
2^45659+1 = 5037282693407580192481
2^45667+1 = 21266391110435514539
2^45673+1 = 24974244078844334538361
2^45673+1 = 87589378942337
2^45691+1 = 34444647603401029764433
2^45697+1 = 882581713267
2^45707+1 = 18584875708471727756641
2^45757+1 = 5098421208222289640815337
2^45763+1 = 1108355927545011584373841
2^45767+1 = 5852704178315872217
2^45779+1 = 7319381890783808081
2^45823+1 = 1796201532422903867
2^45823+1 = 23541704328031162266259681
2^45823+1 = 525828047893122458881
2^45827+1 = 25074451603071363912371
2^45827+1 = 693888955307115855924653016563
2^45833+1 = 82883043859254674731
2^45853+1 = 5200609142397297227299
2^45863+1 = 686736416270823462873361
2^45869+1 = 10181089648651643339
2^45869+1 = 527415823299357850280257
2^45887+1 = 160473239961179
2^45893+1 = 531104727883
2^45949+1 = 40160911473620534972329
2^46091+1 = 16412139014380742984368579
2^46093+1 = 654986077369334616993097
2^46099+1 = 641754770787652535145299
2^46103+1 = 10210230110838678352540219
2^46103+1 = 589432718728400939971
2^46103+1 = 6084939274422679082449
2^46147+1 = 10693014154573331744458579
2^46183+1 = 83028575398819
2^46187+1 = 478322548392001
2^46199+1 = 125853371230879731839137
2^46199+1 = 3712119920290720721
2^46219+1 = 988537546247209339
2^46229+1 = 10882240030241
2^46229+1 = 4158277140040140394380193
2^46271+1 = 488639309294713
2^46279+1 = 15137152707943191862815883
2^46307+1 = 164198193338759299
2^46307+1 = 639816653719159619713
2^46327+1 = 1422497478332536410587
2^46337+1 = 1722322174763545673
2^46349+1 = 51256354454883975337
2^46381+1 = 1843701330173087611
2^46411+1 = 2077094438752113293521
2^46439+1 = 128037554910619
2^46447+1 = 350128530644047185473
2^46471+1 = 241771625858206868729
2^46499+1 = 24908492040970792931
2^46523+1 = 192898661199880033997424179
2^46523+1 = 356855028335876209
2^46567+1 = 7947822740914932756329
2^46573+1 = 418738799297194609
2^46591+1 = 479818171004059873
2^46633+1 = 30079504559332212029871377
2^46649+1 = 194024013569
2^46649+1 = 30289578987216793
2^46649+1 = 3406698407099149153
2^46649+1 = 442890985282787
2^46663+1 = 24184236186581539
2^46687+1 = 967559544007986691
2^46703+1 = 11244283680659
2^46703+1 = 379856795569
2^46723+1 = 6132098460641
2^46747+1 = 970828780358939050029017939
2^46747+1 = 97159245283
2^46757+1 = 42271320449
2^46769+1 = 1934434369449749952457
2^46769+1 = 8299992377426199727897
2^46807+1 = 800417153394161
2^46811+1 = 1244294351915018497969537
2^46829+1 = 203040394644015492102113
2^46831+1 = 3141191957021773586211971
2^46853+1 = 20758268128177
2^46867+1 = 279141065575822705601
2^46867+1 = 800839679249936267
2^46901+1 = 43900895614369462257409
2^46901+1 = 6882805157909752756793
2^46933+1 = 23032739958671317577
2^46957+1 = 125483982735696582916601
2^46993+1 = 14479587117430434222539[/CODE]

 axn 2018-12-26 10:03

10k-10.5k done to t35. Just the one factor
[CODE]ECM found a factor in curve #1308, stage #2
Sigma=4867887659600039, B1=1000000, B2=100000000.
2^10247+1 has a factor: 37196184638687822890576519393981019 (ECM curve 1308, B1=1000000, B2=100000000)
[/CODE]
Currently working on 9.5k-10k. I've excluded already done ones (here as well as M+2)

 axn 2018-12-27 16:19

47k-50k
[CODE]2^47051+1 = 9660268240550759735537
2^47057+1 = 1940788329511150877843
2^47057+1 = 2196284066326812506341667
2^47059+1 = 31441308995228014833082969
2^47093+1 = 27447671596694891329
2^47111+1 = 183658262984921
2^47119+1 = 1245559738631188910166827
2^47123+1 = 1566764693373676714434659
2^47137+1 = 243305426945081616707
2^47137+1 = 449380174233815110768049
2^47161+1 = 266054441407387799657137
2^47189+1 = 2422998219178147182892939
2^47207+1 = 66489643291
2^47207+1 = 68285280473886227
2^47251+1 = 6251876787667287467
2^47279+1 = 107150856209
2^47287+1 = 2292589120811596715753
2^47293+1 = 18535451841228695200559387
2^47293+1 = 631192430233
2^47293+1 = 80584974695233
2^47297+1 = 17413278687189095472815483
2^47303+1 = 1089864065063172273419
2^47303+1 = 1239903492427
2^47303+1 = 4751950906936339
2^47303+1 = 5809550773283
2^47339+1 = 305475539479605763
2^47339+1 = 432708807637619331353
2^47351+1 = 19631197283235357221147
2^47389+1 = 344657367573059437067
2^47389+1 = 44356760722853201892803459
2^47407+1 = 76976258301153803
2^47419+1 = 3856086430523
2^47419+1 = 430144831799251969
2^47419+1 = 6557111017116446444103451
2^47431+1 = 11064837275956979
2^47459+1 = 105511706269469057
2^47501+1 = 37414447657
2^47513+1 = 143950801283
2^47513+1 = 3956034342899
2^47563+1 = 355122363254563081
2^47563+1 = 5004527808824707
2^47581+1 = 6140547449678260781849641
2^47599+1 = 1131989025809729760980257
2^47599+1 = 1595058695405221977209
2^47609+1 = 3785944997017
2^47653+1 = 411894535945193137
2^47681+1 = 58311958144051
2^47701+1 = 33264983776316313937
2^47701+1 = 507794659140336257
2^47701+1 = 70915474973402531
2^47713+1 = 302197239618072844884859
2^47737+1 = 3339620891642711584523
2^47743+1 = 1259158935155804171
2^47743+1 = 3909086840129
2^47743+1 = 9274554702571
2^47779+1 = 157697768293883558371291
2^47791+1 = 3445581131843
2^47797+1 = 366307695171657338849
2^47809+1 = 13389552716107
2^47809+1 = 39236988752130019598089
2^47819+1 = 1572608055283
2^47819+1 = 205451081809
2^47819+1 = 3344934883353727759283
2^47819+1 = 34456363003
2^47837+1 = 126790865756118257
2^47837+1 = 155406506604595210337
2^47837+1 = 38626845788727593
2^47843+1 = 10612334035518999673
2^47843+1 = 58939906647659
2^47857+1 = 6029532819720463970699
2^47881+1 = 4810528992593
2^47903+1 = 1928199704243632188091
2^47911+1 = 2355878045298931
2^47917+1 = 5597587336529611
2^47947+1 = 2845739925308689
2^47951+1 = 81495576898066384191043963
2^48017+1 = 1052374274556097
2^48023+1 = 155444544508558277209
2^48029+1 = 20335497523427
2^48029+1 = 5199893209243
2^48119+1 = 482864990342747
2^48157+1 = 1201958286508974948687857
2^48259+1 = 44005493924133626512073
2^48281+1 = 237432299208539
2^48311+1 = 26760521016886819368142392371
2^48313+1 = 568039890720361
2^48341+1 = 4044104416897
2^48353+1 = 217134666962011
2^48397+1 = 133199094547
2^48409+1 = 20781371422969
2^48413+1 = 699552357841
2^48449+1 = 13905669519359731
2^48449+1 = 5066634503443
2^48463+1 = 82641046121
2^48479+1 = 112407112336191298559641
2^48481+1 = 387326197645081038299
2^48487+1 = 3169097762630379329
2^48527+1 = 75057392064181817
2^48533+1 = 15849347250485142377689
2^48541+1 = 276656679357290716123
2^48593+1 = 160654021020048574553
2^48593+1 = 176579284307
2^48619+1 = 93600626911827896041
2^48649+1 = 209689254953
2^48661+1 = 2027824582051431760836049
2^48677+1 = 17923323613583710650619975646899
2^48677+1 = 683017613010737
2^48679+1 = 273780452516224673
2^48679+1 = 35433541459
2^48731+1 = 5626646643657649
2^48779+1 = 838972305881267
2^48781+1 = 1578277440078038534281
2^48787+1 = 56390517679978816513
2^48821+1 = 109601942753238309593
2^48823+1 = 2848130706441945405539
2^48847+1 = 957119472289763
2^48859+1 = 5871975456844314546881
2^48859+1 = 8898391455452815102148387
2^48869+1 = 134745608199975233
2^48869+1 = 1640790413673329873
2^48869+1 = 17930169051961565419
2^48907+1 = 7297876619291
2^48953+1 = 1402976200903791289
2^48973+1 = 1968639486192060001
2^49003+1 = 70196833969637087881939
2^49031+1 = 1995218861421259
2^49031+1 = 325869344243489
2^49033+1 = 9562136000701955419729867
2^49121+1 = 424725315953
2^49139+1 = 14291281311977
2^49169+1 = 61605651271931884123459051
2^49177+1 = 2992448678689596825496073
2^49199+1 = 427706995126286784217
2^49201+1 = 173850355873
2^49201+1 = 18914755810885294232491
2^49211+1 = 44692098514719577855033
2^49253+1 = 124570660388591209310131
2^49261+1 = 29844941050715438506259
2^49261+1 = 6124591867692780289667
2^49279+1 = 11079167459383136969
2^49331+1 = 5573474173911384698011811
2^49333+1 = 16542541654649
2^49333+1 = 266875348777
2^49339+1 = 137244585841598993
2^49391+1 = 72597954043
2^49409+1 = 529182460816337
2^49429+1 = 1780351977890048984153
2^49429+1 = 32828028233143276241
2^49433+1 = 14579583226696458739001
2^49433+1 = 283022805144481942387
2^49433+1 = 82431378714613027294297
2^49459+1 = 1614652977018744922739
2^49459+1 = 4040349569128453513843
2^49459+1 = 407675115668665547
2^49463+1 = 27714596910433
2^49481+1 = 840054078187
2^49499+1 = 24343154066888421298244881
2^49499+1 = 6284577307650347
2^49531+1 = 33806342214947
2^49549+1 = 11133455692359401
2^49603+1 = 129888372779016857
2^49613+1 = 508805228467
2^49639+1 = 8070980428355646092843
2^49669+1 = 736646255197575480977
2^49711+1 = 10672751373419137
2^49727+1 = 22480536411161
2^49739+1 = 102376082071112761
2^49741+1 = 3561380642880257263019
2^49741+1 = 4106080739684233
2^49757+1 = 2008254511298226844008841
2^49801+1 = 4892010795977
2^49843+1 = 4320093234185731
2^49853+1 = 96735100947796177
2^49871+1 = 2254685885403499
2^49871+1 = 5384353718187539
2^49877+1 = 183701779193
2^49877+1 = 320654471141559691
2^49891+1 = 2925672121191589032208403
2^49891+1 = 6225057927418987
2^49957+1 = 12056609591009
2^49991+1 = 34022296194464147
2^49993+1 = 14793999369835576177428473[/CODE]

 axn 2018-12-29 12:32

50k-54k
[CODE]2^50021+1 = 21195204612072813361419113
2^50069+1 = 1906908988806244223299
2^50087+1 = 109594427211021993670699747
2^50087+1 = 55080052212470922907483579
2^50101+1 = 48951592027878713659
2^50129+1 = 807745687130539
2^50131+1 = 3501967327054548573203
2^50153+1 = 141430741495647096950323
2^50159+1 = 172626179213047231307
2^50177+1 = 240766881108067
2^50221+1 = 44611935729314989519723
2^50273+1 = 277960458174743569
2^50273+1 = 34877297878331702219
2^50329+1 = 46911419593267006075283
2^50329+1 = 4860308497544292409027
2^50387+1 = 327237541063690307
2^50417+1 = 9084581805318528529
2^50423+1 = 458209496167211
2^50441+1 = 1624228487607476323
2^50461+1 = 953074681288881847249
2^50497+1 = 806291657428073
2^50539+1 = 25874544060385602841265517331
2^50543+1 = 5782828646397952597412513
2^50549+1 = 11563687093848794516273
2^50551+1 = 82333826887175273
2^50647+1 = 339085896103788578323
2^50647+1 = 74165448182779801
2^50651+1 = 4886928941818057059617
2^50671+1 = 27121972490089771183963
2^50671+1 = 758211397759892697923
2^50741+1 = 516937037303971
2^50767+1 = 30199735598847250123
2^50767+1 = 31934738721431756083
2^50767+1 = 3793376452857515033593
2^50767+1 = 641954481946116920489
2^50821+1 = 11646399244796532732289
2^50833+1 = 1482034930387769
2^50849+1 = 341092459496421001
2^50857+1 = 37105879703335298467
2^50857+1 = 42904075021796801
2^50867+1 = 5914340677932257
2^50957+1 = 55324229628172429283
2^50969+1 = 146400275377844089547052979
2^50989+1 = 1641804996603061631729
2^50993+1 = 16163227063616878403
2^51031+1 = 34726073052342377929
2^51061+1 = 116717625902895336466627867
2^51061+1 = 117926544126307949371
2^51061+1 = 96737410516026961
2^51133+1 = 10211906404447062691
2^51137+1 = 25431470121033233
2^51169+1 = 3148378148830731466651
2^51169+1 = 384182421834668041237537
2^51197+1 = 25773522584361521
2^51197+1 = 33621365793311773872257
2^51229+1 = 1732038725598839297
2^51229+1 = 8465121218826462848221427
2^51283+1 = 11979455483819173249
2^51287+1 = 27754986598517399017
2^51307+1 = 201414822034036653209052001
2^51341+1 = 419250931235890939
2^51347+1 = 228299183797897
2^51361+1 = 33381181373063716531
2^51383+1 = 73013531213810327560811297
2^51421+1 = 5556566979122801
2^51431+1 = 981461495594665196266354153845143093297
2^51461+1 = 521461293581729
2^51473+1 = 31765776698501201
2^51481+1 = 10395569553574420818859
2^51481+1 = 3009238233309908340787393723
2^51481+1 = 59875229392336831802281
2^51487+1 = 273227338438939
2^51487+1 = 360003258755411892443
2^51503+1 = 2608187702720548073611
2^51517+1 = 2165480183790739
2^51521+1 = 2782443640901698337
2^51593+1 = 1148923720544412961
2^51593+1 = 241024517143358297
2^51599+1 = 152048900923503760825644577
2^51631+1 = 833577177515049041
2^51637+1 = 771184674341389229349341609
2^51647+1 = 258835676982137579
2^51673+1 = 168436973726692219
2^51679+1 = 21978485800397600563
2^51691+1 = 374365616936595275617
2^51719+1 = 3265379868048802004434249
2^51769+1 = 392978648837626459
2^51803+1 = 9003959218598407691
2^51827+1 = 3759770382123348107
2^51827+1 = 774879518219012967577
2^51853+1 = 587554052162505299109659
2^51971+1 = 151372304289259897
2^51977+1 = 2483555275031757756240306521
2^51977+1 = 2630060460419537507
2^52009+1 = 24897904934127969203
2^52021+1 = 744553086142753
2^52051+1 = 247515502730059339
2^52051+1 = 521291336624083
2^52051+1 = 791255655590788819
2^52051+1 = 89132981568654467
2^52121+1 = 209542908390786721
2^52147+1 = 396090131937553
2^52163+1 = 202838692239464782551821257
2^52189+1 = 7822273812268942668427
2^52201+1 = 40632439627315001
2^52201+1 = 76574701084247663450443
2^52237+1 = 223345356452692111538865953
2^52237+1 = 394382814998292498827
2^52249+1 = 234073323974531
2^52253+1 = 137433444774032513
2^52259+1 = 10401782725859323754177
2^52259+1 = 87536023104157524073
2^52267+1 = 191573670125403803
2^52267+1 = 21375577852639383079547083
2^52267+1 = 95718126037171839449
2^52301+1 = 9552833185873176627218441633
2^52369+1 = 6871701399048062099
2^52391+1 = 10995954993763275781561
2^52391+1 = 3440208563238377418922006897
2^52453+1 = 3911208679153187632256539
2^52489+1 = 232304709985611827
2^52501+1 = 240893344040193353306899
2^52511+1 = 487979566029126141673
2^52529+1 = 3381999442429852679899
2^52541+1 = 45305525124667746652849
2^52543+1 = 190117131394540760209
2^52553+1 = 9950176977387841
2^52567+1 = 31447612432774236011
2^52567+1 = 3325738607190347521
2^52583+1 = 157797812851997472073
2^52609+1 = 129210946547718433
2^52673+1 = 490351307851817
2^52691+1 = 8447912334225568653851
2^52711+1 = 67154343230563531
2^52733+1 = 1216912682966632027
2^52837+1 = 5197231212224531608692049
2^52837+1 = 9335362023317306686777
2^52861+1 = 75946147667215548343129
2^52879+1 = 1454885836863937
2^52879+1 = 718899351469009
2^52883+1 = 744736778959412564243
2^52889+1 = 563976368069709547
2^52903+1 = 269201506210729
2^52919+1 = 8711554481912461171
2^52951+1 = 866463568936643
2^52967+1 = 11856373072431217441
2^53051+1 = 840967579356451
2^53069+1 = 11999639725450483
2^53069+1 = 40005455631097068670979
2^53089+1 = 5200508009243659760532691
2^53113+1 = 6844116852765315787
2^53161+1 = 1111616143526843
2^53171+1 = 5388177134823500953224019
2^53173+1 = 3906409021022779
2^53197+1 = 6781214632378290426413233
2^53201+1 = 8599957351880562832767401
2^53231+1 = 259729396050473464603
2^53231+1 = 571984499271333831795947
2^53239+1 = 330946139317643
2^53279+1 = 2619302002561013179
2^53353+1 = 222921801993717781856383721
2^53407+1 = 127834702674056800561
2^53437+1 = 16007061540426626612161
2^53441+1 = 408186592603810379
2^53527+1 = 75177939207480858739
2^53549+1 = 110726595312517081
2^53623+1 = 340608278314007925725633
2^53629+1 = 1142838777601945812802129
2^53653+1 = 104890937448132883
2^53653+1 = 1797922429499666445203
2^53657+1 = 71184039555890032019
2^53681+1 = 1999028738602393272781099
2^53699+1 = 991053493763689630531
2^53719+1 = 3634049204726017274531
2^53759+1 = 37569489837321725603
2^53759+1 = 8161226538660983784977
2^53791+1 = 4129394377417621067195291
2^53881+1 = 34321408852291898299
2^53899+1 = 1895695607453941193
2^53899+1 = 31716634355791362281478491
2^53899+1 = 58895608986317267
2^53923+1 = 873719251388827094267
2^53951+1 = 235394627504576609
2^53987+1 = 6555210473133043
2^53993+1 = 257994912583169[/CODE]

And...
[CODE]ECM found a factor in curve #27, stage #2
Sigma=6998648846391097, B1=50000, B2=5000000.
2^53759+1 has a factor: 37569489837321725603 (ECM curve 27, B1=50000, B2=5000000)
ECM found a factor in curve #3, stage #2
Sigma=2526292520113682, B1=50000, B2=5000000.
2^53759+1 has a factor: 8161226538660983784977 (ECM curve 3, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
Thus, (2^53759+1)/3 = 59672491 · 37569489837321725603 · 8161226538660983784977 · PRP16134

 paulunderwood 2018-12-29 12:44

[QUOTE=axn;504268]
Thus, (2^53759+1)/3 = 59672491 · 37569489837321725603 · 8161226538660983784977 · PRP16134[/QUOTE]

Congrats :toot:

[CODE] time ./pfgw64 -k -f0 -od -q'(2^53759+1)/3/59672491/37569489837321725603/8161226538660983784977' | ../../coding/gwnum/bpsw-2 - 1 2 53759 1

Testing (2*x)^((n + 1)/2) == 2 (mod n, x^2 - 3*x + 1)...
Likely prime!

real 0m1.758s
user 0m1.920s
sys 0m0.004s
[/CODE]

 axn 2019-01-03 13:51

54k-60k
[CODE]2^54037+1 = 48843995860005435776889947
2^54049+1 = 20124656586239469643
2^54059+1 = 1289462690717161
2^54059+1 = 230452591072258337
2^54083+1 = 1209734892615918323
2^54091+1 = 153618141157610473
2^54101+1 = 1647337889610351761
2^54101+1 = 24537640514842004355467
2^54133+1 = 123914471977619271307
2^54133+1 = 50567978459004375097
2^54139+1 = 916823344984382861716883
2^54151+1 = 700503785298324817
2^54181+1 = 30770630234099659
2^54181+1 = 680085442230396913
2^54251+1 = 319981328040107
2^54269+1 = 235723501849082113455707
2^54277+1 = 225890972324310387139
2^54331+1 = 8266938645428219353
2^54371+1 = 339752542977011
2^54377+1 = 1390718683893467
2^54401+1 = 1413762693938299
2^54401+1 = 235390703916627709323089
2^54401+1 = 4025413363176971
2^54421+1 = 4572632954162191049
2^54421+1 = 539444105073698350601
2^54437+1 = 300901362168899383009787
2^54469+1 = 7724654792661187
2^54521+1 = 6403894493983259024670329
2^54539+1 = 12825731145449814630593
2^54541+1 = 536506555953360181169
2^54547+1 = 1367184321264170209
2^54547+1 = 1963879707027307
2^54547+1 = 24038107600360763366459
2^54577+1 = 2511983725891143778399714489
2^54583+1 = 83518756578290082214657
2^54629+1 = 12631940281855568689
2^54647+1 = 64324092844644034313
2^54667+1 = 42049634129653199939
2^54667+1 = 81221808280239377
2^54673+1 = 3133585417259035471219
2^54709+1 = 3799442627622749492323
2^54709+1 = 4696884997099683728849
2^54713+1 = 583485688148229740299
2^54751+1 = 4119393249671220667
2^54779+1 = 2218069999852581755351689
2^54787+1 = 1557817321824385289
2^54799+1 = 126865403903317747
2^54829+1 = 21721488624444734796379
2^54881+1 = 4373485056399530209
2^54907+1 = 25993316589305375402285731
2^54907+1 = 27524111168391907
2^54919+1 = 1434106979001017
2^54941+1 = 6926911094253433
2^54949+1 = 38396301233096643553
2^54983+1 = 17689320715773215527867
2^54983+1 = 579556590123821153909587
2^54983+1 = 836047467789817
2^55001+1 = 1004832644528315929
2^55001+1 = 34816126541516602528793
2^55001+1 = 629626874292354913765907
2^55073+1 = 281286952933664408024939
2^55079+1 = 4626455842132968674819
2^55103+1 = 4623846041128137980520577
2^55117+1 = 182763683383511548539779
2^55127+1 = 42945899321103662152992923
2^55171+1 = 12612269264478607968019907
2^55171+1 = 236636829156899
2^55213+1 = 47049166246538971937
2^55217+1 = 220615500896492929
2^55219+1 = 709762262952973486209091
2^55229+1 = 2878563417037361
2^55243+1 = 110965694216487635281
2^55243+1 = 2616423609070094667813019
2^55259+1 = 49573160602208118131
2^55333+1 = 54861964167039001800483043
2^55337+1 = 12364668501099371
2^55343+1 = 100069674863199491
2^55343+1 = 99644867301925421363
2^55373+1 = 11082554819541856649730187
2^55381+1 = 37584037351921648780211
2^55411+1 = 173143924096576913
2^55439+1 = 180321577095959734758377
2^55469+1 = 2953741271882969
2^55469+1 = 600824060741613889681
2^55487+1 = 10215078261339897083
2^55609+1 = 142115669584424375907083
2^55639+1 = 29142985272710053045891
2^55661+1 = 3400990925581189831549531
2^55661+1 = 41970073911374242980933443
2^55681+1 = 554065761719893777
2^55691+1 = 15943323848245524973681
2^55691+1 = 4852325147305338299
2^55697+1 = 1516005295717259529617
2^55697+1 = 681316729651307644571
2^55711+1 = 2096660511843012827
2^55717+1 = 71918900084275349929
2^55721+1 = 105949759979105921
2^55733+1 = 4584148227670909646963
2^55763+1 = 284101606496682200736721
2^55787+1 = 22671743002726598017
2^55799+1 = 1728418811769289597681
2^55807+1 = 107118354958504495231057
2^55807+1 = 2325065915036923
2^55813+1 = 85645723205813969467
2^55817+1 = 333782684171636018247857
2^55819+1 = 377805036039481
2^55819+1 = 7524650880976555049
2^55849+1 = 401117823251224913
2^55889+1 = 788885859319099
2^55897+1 = 27744431344008421961
2^55903+1 = 212434183569025732763
2^55903+1 = 5385999012463969
2^55933+1 = 18054067908947561
2^55949+1 = 210154351527696193
2^55949+1 = 7679236226578579919202159971
2^55967+1 = 2637693914717921
2^55987+1 = 56578345986287274506299
2^55987+1 = 9880738802927929
2^56009+1 = 3013416159632214187
2^56041+1 = 125261284818709003
2^56041+1 = 230008157675929
2^56081+1 = 1058808037245041
2^56087+1 = 7136570818188979
2^56113+1 = 2276065844887697827
2^56131+1 = 94470417629643667
2^56179+1 = 205961650611347
2^56237+1 = 86477979738156577
2^56263+1 = 206148619768521974328203
2^56393+1 = 197450158162591148196313
2^56467+1 = 24137564192758544063105539
2^56467+1 = 3841991159698540299643
2^56473+1 = 576235703754329
2^56479+1 = 713738903694250579
2^56503+1 = 1135039701578704466563
2^56503+1 = 2063738247063567430099
2^56509+1 = 15841600865522195164241
2^56509+1 = 9041105588916078763
2^56519+1 = 11864199778635888746761
2^56531+1 = 1033079152756428763
2^56543+1 = 3509234745241378840387
2^56629+1 = 1771742405205364149373441
2^56711+1 = 178417328314392343638740772523
2^56783+1 = 26974278954243787571
2^56813+1 = 505949168962659473
2^56827+1 = 474673425712066011889
2^56891+1 = 1962701841550076266049
2^56897+1 = 8594193363144294336535875142825115131379
2^56909+1 = 165497815690827112459
2^56957+1 = 687855156763193
2^56963+1 = 74407481210104918636027
2^57041+1 = 392874323459543830775977
2^57047+1 = 232601466141587
2^57047+1 = 3913950898407371
2^57047+1 = 605479254284721013836193
2^57059+1 = 5473443712317017
2^57077+1 = 241486304719838464219
2^57077+1 = 86820410332577401171
2^57089+1 = 9881747222211924703321
2^57107+1 = 12234369383136338587
2^57119+1 = 60218217523788059
2^57131+1 = 2663829467981369
2^57131+1 = 33367140968173884744019507
2^57131+1 = 3337670412229893673
2^57163+1 = 3203360562701041
2^57179+1 = 192941363126984138750443
2^57191+1 = 13509819180006209147
2^57193+1 = 24956867300124042845528363
2^57221+1 = 913614353282965819
2^57241+1 = 975048725768521396217
2^57251+1 = 210092442198675477042693089
2^57251+1 = 5300002359288138104203
2^57269+1 = 1266155246666052289
2^57269+1 = 8396761993477241
2^57269+1 = 8827687029082483
2^57271+1 = 5540276616224772403
2^57389+1 = 44779706918216109262483
2^57389+1 = 495337845439229993
2^57389+1 = 5830693344238655339
2^57397+1 = 139305660090940107683
2^57397+1 = 57699389749464146617
2^57467+1 = 1282466273830240691
2^57493+1 = 32707537633693197227
2^57493+1 = 518874301340020697
2^57503+1 = 178808916427841214168801139
2^57587+1 = 1177059310796130401
2^57653+1 = 1451208060020011
2^57713+1 = 461866655429417512807553
2^57773+1 = 12016997114891137
2^57773+1 = 7259318753841326272417
2^57781+1 = 100084945000747036091
2^57781+1 = 150613099022157763
2^57787+1 = 24239365096399891
2^57793+1 = 201428745537783889
2^57793+1 = 3556922678129119890817
2^57803+1 = 26825627070229704833
2^57803+1 = 69419571411390862703203
2^57847+1 = 271559760203882662318786387
2^57881+1 = 284227198678078441732907
2^57917+1 = 10764015047869104567563
2^57917+1 = 2010778864531555408914870569
2^57977+1 = 2099941688225437649
2^57977+1 = 444947379253706506739
2^58013+1 = 1604901501385363
2^58027+1 = 39025206767354727307
2^58043+1 = 11765187577581614283841
2^58061+1 = 385244321219467
2^58067+1 = 772857329317771
2^58067+1 = 7893011718064619
2^58099+1 = 1169378231842433
2^58099+1 = 1604844067686118226017
2^58099+1 = 2121695885648179
2^58111+1 = 51027593198335358593
2^58129+1 = 9214804898790096409003
2^58129+1 = 9553209035695588537
2^58169+1 = 105239554696256107
2^58211+1 = 3888827660412365838684883
2^58211+1 = 51848505124889785337803
2^58217+1 = 2988719610586100243681
2^58237+1 = 1279067812270351071628865419
2^58271+1 = 25432206060430430761
2^58271+1 = 360750874076363051
2^58271+1 = 837359100177143713019
2^58313+1 = 115659494248120346950891
2^58313+1 = 572921908317154003
2^58363+1 = 10213924878880267
2^58369+1 = 225169143999730811
2^58369+1 = 4029998424639233
2^58369+1 = 528357205855082059
2^58379+1 = 2363844302477837059
2^58379+1 = 29333472073149371
2^58379+1 = 327818582024372798939
2^58379+1 = 931810865187733243129
2^58393+1 = 28921196257411682741849
2^58403+1 = 169445782739864659241
2^58403+1 = 18453278158807901728617611
2^58403+1 = 31032600768149928601
2^58417+1 = 13533869202558829361
2^58417+1 = 180698068396193
2^58417+1 = 2484321432878794497823883
2^58427+1 = 2717282223113603
2^58427+1 = 6488451566429349971
2^58441+1 = 1647031362498352843
2^58441+1 = 20903315642310401
2^58451+1 = 477022191825163
2^58453+1 = 221493381287504099
2^58453+1 = 862907624147147
2^58481+1 = 392166789852344953
2^58537+1 = 1748775412729800956539
2^58537+1 = 1915244822884817
2^58549+1 = 2516859212029484825219
2^58603+1 = 534188239901243
2^58631+1 = 2498644841439059155265587
2^58711+1 = 60160961374513753483
2^58733+1 = 11323563806077317859
2^58733+1 = 75453626218790102617
2^58757+1 = 3991192573896183135331
2^58771+1 = 635763772130333761
2^58787+1 = 331741418901684063113
2^58787+1 = 4973034012941514907
2^58789+1 = 239170468933132843
2^58789+1 = 3470978136312412771
2^58897+1 = 35718268998614819626787
2^58897+1 = 9733367778620560849
2^58901+1 = 21285568508658724489
2^58909+1 = 98105451585964169
2^58921+1 = 2224740281718503449
2^58943+1 = 2342900041646333626938713
2^58979+1 = 985454664510451
2^59011+1 = 29251200538799783342419
2^59021+1 = 1109319445315273
2^59021+1 = 55477154848504896707
2^59051+1 = 119155629283676279602993
2^59053+1 = 9450369236080037765603
2^59077+1 = 65653548258897499
2^59083+1 = 2355296547506561
2^59093+1 = 1205994570213067337
2^59093+1 = 59859698429278201
2^59093+1 = 60267430541357735535451
2^59113+1 = 4829188723578019
2^59113+1 = 516744037204459
2^59119+1 = 450122567720677556521331
2^59119+1 = 61602188114907641053311381898145416451
2^59123+1 = 404722643418061027858616593
2^59123+1 = 592349073403979
2^59167+1 = 14023367944611401
2^59197+1 = 13783864150429267
2^59197+1 = 147686300455733820833779
2^59197+1 = 368080211808121819
2^59209+1 = 381340122397570291
2^59221+1 = 1200801042891113668464899
2^59233+1 = 1006858246373394813044513
2^59243+1 = 105990540949622824645879627
2^59273+1 = 101538562508478859
2^59333+1 = 3216861339965751001
2^59333+1 = 5035771476157102763
2^59357+1 = 165903541529681
2^59357+1 = 1990826076411113
2^59369+1 = 56382027291031626473
2^59369+1 = 914301287943468281
2^59399+1 = 142400141325610248713
2^59407+1 = 10468366314853609
2^59441+1 = 21101360863054861921993
2^59441+1 = 5471158890228384481
2^59447+1 = 24535026225311449
2^59453+1 = 1787939506999535582137
2^59471+1 = 657608720887020953
2^59473+1 = 94191516708803089
2^59513+1 = 77231819904279790508179
2^59561+1 = 186360907334162408096969969
2^59561+1 = 39106947788574946601
2^59581+1 = 9702323062597273
2^59617+1 = 74777843483494211
2^59621+1 = 11550150279731882203337
2^59651+1 = 33769035419031713
2^59663+1 = 229910242356729235423867
2^59663+1 = 3555131586302944577
2^59669+1 = 20684790440635175003
2^59669+1 = 243615294794630825267
2^59669+1 = 6710962505723512313
2^59671+1 = 391886505396956729
2^59693+1 = 12069151210664672819
2^59693+1 = 1431236790854947
2^59693+1 = 184946558714995633
2^59693+1 = 272332660577464742467
2^59699+1 = 14557472274186761
2^59699+1 = 688555859503197763219
2^59707+1 = 20491784540092885339
2^59753+1 = 49987378984871105504249
2^59779+1 = 2281076125894840363
2^59797+1 = 93961281914907858827
2^59833+1 = 1715373024332083
2^59887+1 = 96650462655278404337
2^59951+1 = 1836095011749178307
2^59951+1 = 3148540622252762761
2^59951+1 = 59369484527768709449
2^59957+1 = 142582080049717783043
2^59971+1 = 124801859883416747
2^59981+1 = 1291951161801753914698049[/CODE]

 axn 2019-01-05 05:55

[CODE]ECM found a factor in curve #11, stage #2
Sigma=4386452412346322, B1=50000, B2=5000000.
2^62581+1 has a factor: 3746586115387179252611 (ECM curve 11, B1=50000, B2=5000000)
ECM found a factor in curve #1, stage #2
Sigma=7031221505242364, B1=50000, B2=5000000.
2^62581+1 has a factor: 330100331790953723 (ECM curve 1, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
Thus, (2^62581+1)/3 = 1958759661815921 · 330100331790953723 · 3746586115387179252611 · PRP18784

 paulunderwood 2019-01-05 05:59

[QUOTE=axn;505003][CODE]ECM found a factor in curve #11, stage #2
Sigma=4386452412346322, B1=50000, B2=5000000.
2^62581+1 has a factor: 3746586115387179252611 (ECM curve 11, B1=50000, B2=5000000)
ECM found a factor in curve #1, stage #2
Sigma=7031221505242364, B1=50000, B2=5000000.
2^62581+1 has a factor: 330100331790953723 (ECM curve 1, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
Thus, (2^62581+1)/3 = 1958759661815921 · 330100331790953723 · 3746586115387179252611 · PRP18784[/QUOTE]

Congrats :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^62581+1)/3/1958759661815921/330100331790953723/3746586115387179252611" | ../../coding/gwnum/bpsw-2 - 1 2 62581 1

Testing (2*x)^((n + 1)/2) == 2 (mod n, x^2 - 3*x + 1)...
Likely prime!

real 0m2.226s
user 0m2.392s
sys 0m0.012s
[/CODE]

 axn 2019-01-05 12:42

60k-63k
[CODE]2^60013+1 = 10622498326640071325929
2^60013+1 = 21235164036950971
2^60029+1 = 141314942210915112049
2^60029+1 = 14365965199172414347753
2^60029+1 = 80084521199508240089
2^60037+1 = 1344227040302218758702179
2^60037+1 = 1863129603863080019
2^60037+1 = 2847187507574801
2^60041+1 = 2869077318697158838187
2^60041+1 = 7935253562567490494963
2^60091+1 = 45634402396521148503353
2^60101+1 = 776313743932821387140483
2^60103+1 = 3192305561962843
2^60103+1 = 58882471671899729029433
2^60107+1 = 36489011186238482329
2^60127+1 = 3040518984911440859
2^60169+1 = 480750031417531
2^60223+1 = 1016052460307744987
2^60251+1 = 91941428904101999723
2^60257+1 = 2637965982408049838723
2^60259+1 = 7317946188263223641
2^60289+1 = 71050203952424309771
2^60293+1 = 505804243297312681
2^60317+1 = 87780356386715799695227
2^60397+1 = 5025974352610696776409
2^60457+1 = 369947808526603
2^60509+1 = 20396240340212235394385729
2^60521+1 = 430800369141387433
2^60539+1 = 10309509934845883324975339
2^60589+1 = 407778231901356427
2^60607+1 = 2528885035906137697
2^60607+1 = 474473682371965019
2^60631+1 = 25558554126440731137227
2^60649+1 = 959472379097316131
2^60659+1 = 2349883462647527507
2^60679+1 = 35953324878575724345619
2^60703+1 = 12590561634715387
2^60703+1 = 45118248209027667942883
2^60719+1 = 42087832992593419206427481
2^60757+1 = 4793419974862426846259
2^60773+1 = 15553136921660013839731
2^60779+1 = 250480140387460747
2^60811+1 = 107099142063686147
2^60859+1 = 250899842753474203
2^60887+1 = 11315545789290437900718859
2^60919+1 = 203013696428367971
2^60923+1 = 1071299720791171360012922297
2^60923+1 = 73816636724542258592579
2^61001+1 = 453086242803563
2^61027+1 = 1092048332703757019
2^61031+1 = 239249301908401571
2^61031+1 = 5946914653537341923
2^61051+1 = 3760765335396464563457
2^61057+1 = 979154747509810701614285803
2^61151+1 = 77575900232132921
2^61153+1 = 9683794508973516930259
2^61283+1 = 1599646274413841723
2^61283+1 = 261729678377273
2^61297+1 = 230041435081471291
2^61333+1 = 122093697040952511476551993
2^61357+1 = 584227854365391121
2^61379+1 = 17794008173331883
2^61409+1 = 3380744447532379
2^61409+1 = 436226494246314898361
2^61417+1 = 222682707721106595620487497609
2^61441+1 = 6300445442936140019
2^61469+1 = 1354799257878100852627
2^61469+1 = 63239101727820719938091
2^61511+1 = 1093653941445992683
2^61511+1 = 35976986732571707
2^61511+1 = 45466807817825901539
2^61543+1 = 409958007445049174497
2^61547+1 = 3141045652858871137
2^61631+1 = 7032975205281599883731457761251
2^61637+1 = 1661971505676660311561
2^61657+1 = 196916895913408019
2^61657+1 = 7263374540828172272497
2^61667+1 = 12200006344553779
2^61667+1 = 3581451335047874468267
2^61667+1 = 997307813433907
2^61703+1 = 17846188377544965403326390787
2^61703+1 = 380540646330289
2^61703+1 = 40489713800388655163
2^61717+1 = 7175315091040121
2^61729+1 = 2284108593461138205529
2^61729+1 = 36331683330662695994939
2^61757+1 = 44085423329382955097
2^61819+1 = 16017379052476979
2^61819+1 = 27969898205904957419716680073
2^61909+1 = 11429410459248449
2^61909+1 = 20641734936822725113
2^61927+1 = 67780893401792931977
2^61933+1 = 7518478402199811812622739369
2^61967+1 = 119040030117266977
2^61967+1 = 49163164824047969347
2^61979+1 = 20437316338461356029502689
2^62017+1 = 262636386319052286011
2^62047+1 = 7227172705577383499
2^62047+1 = 8292493510810817089
2^62053+1 = 295298623582928229818474779
2^62099+1 = 2474567254211171929
2^62131+1 = 854250316468193501683
2^62137+1 = 11525180766737113570320353
2^62137+1 = 1397592254604251
2^62137+1 = 14239331818405699
2^62137+1 = 164961090990419
2^62171+1 = 6054654854253996702251
2^62191+1 = 2232545763930587641770139
2^62219+1 = 97401484957275209003
2^62299+1 = 699643095291089
2^62401+1 = 104260322381837876833
2^62417+1 = 9948192300096160793
2^62423+1 = 11256369413120473
2^62459+1 = 839110269596523933974321
2^62477+1 = 3748491523925973390737
2^62477+1 = 39836091741011916089
2^62501+1 = 6003030404449721
2^62507+1 = 139201994098384753
2^62539+1 = 827485637368975027
2^62563+1 = 4887167767253521553
2^62581+1 = 330100331790953723
2^62581+1 = 3746586115387179252611
2^62591+1 = 38741199159855513265403
2^62591+1 = 572057242471967371289
2^62617+1 = 8412429027171963931
2^62633+1 = 2650262527492843739309521
2^62659+1 = 4217725003811083727874451
2^62659+1 = 4727019211972374293033
2^62687+1 = 913305064651938331
2^62743+1 = 506663811556417
2^62753+1 = 149006668283895916633
2^62827+1 = 961777769086588723
2^62861+1 = 516178834391725073
2^62861+1 = 6019210949333683
2^62897+1 = 14658021434042098246801
2^62897+1 = 1558711498348233379
2^62927+1 = 261319465607325666305147
2^62927+1 = 691911801147112129
2^62929+1 = 205899643289639950837600619
2^62939+1 = 1592266582109050382603
2^62939+1 = 53821577177750209369
2^62939+1 = 715815323534566732463969
2^62969+1 = 31347989423467985449
2^62981+1 = 431577658342651
2^62983+1 = 403158714227005416318467[/CODE]

 axn 2019-01-07 17:22

63k-66k
[CODE]2^63029+1 = 696634309814635251379
2^63073+1 = 235651019678932577
2^63079+1 = 2854917660690983219
2^63127+1 = 163627284854439617
2^63127+1 = 333787284109646101235929
2^63131+1 = 5795688532914011
2^63149+1 = 118436974502624836139
2^63149+1 = 221311708850321321
2^63179+1 = 101747462219237953361
2^63241+1 = 91029421450752229653881419
2^63247+1 = 207160540030985336099
2^63277+1 = 75828169865220510889601
2^63281+1 = 356820244124177563
2^63299+1 = 7583698330847494421921
2^63311+1 = 12747451597957864063651
2^63313+1 = 18238998797913787
2^63317+1 = 24192515206225459
2^63337+1 = 340353570696283142595811
2^63389+1 = 143516641316653753
2^63391+1 = 9330954590288010521
2^63421+1 = 41804091224135113
2^63463+1 = 5623233816603439825495753
2^63473+1 = 108147019846616587
2^63527+1 = 64253025578202163621769
2^63533+1 = 155088650542800187
2^63559+1 = 3548239563729587
2^63589+1 = 84468574091829841
2^63607+1 = 42713408662472081727617
2^63629+1 = 18118083331085118107
2^63667+1 = 83685657856456259
2^63691+1 = 3938763945967128683
2^63719+1 = 119325889220861663521
2^63727+1 = 160771335659593
2^63727+1 = 20424493601794907
2^63727+1 = 52518617657730569
2^63727+1 = 710937649684526660243
2^63743+1 = 159281514646907
2^63799+1 = 17099599148442634651907393
2^63803+1 = 2810101363089913
2^63839+1 = 10524371439589369
2^63841+1 = 1443862667864061619
2^63857+1 = 125421316817540245603
2^63863+1 = 2815348261695449
2^63913+1 = 453409128993859
2^63929+1 = 606152239831051
2^63977+1 = 502772955076603
2^63997+1 = 862217354901183643
2^64007+1 = 4745537848213366681
2^64037+1 = 4325576442297915095446691
2^64063+1 = 2685836417856090881
2^64081+1 = 100357417925229413218969123
2^64091+1 = 83474949229422126097
2^64109+1 = 1320424337489386543363
2^64151+1 = 112058705693115862995034543733065342527211
2^64157+1 = 2102633626369165163
2^64157+1 = 36741129757030862909553881
2^64157+1 = 783583326674377
2^64231+1 = 3835667478062219726489
2^64279+1 = 600020909395109895659
2^64301+1 = 50308112377956260746201
2^64373+1 = 148493123847116978775731
2^64373+1 = 9196460607830645447633
2^64381+1 = 2145581331546439273
2^64399+1 = 270440728466409848563297
2^64403+1 = 13499391380645479015526363
2^64439+1 = 1075377076257882039259
2^64451+1 = 522975256676833889
2^64453+1 = 830169255362281
2^64483+1 = 28985740181987489233
2^64489+1 = 17333558388858853091
2^64489+1 = 799018999063100929123
2^64591+1 = 1282621261225277546737
2^64601+1 = 43238353180408779195043
2^64609+1 = 49508039803588489
2^64613+1 = 53117660944031541671969
2^64627+1 = 35092382992625921
2^64633+1 = 1592578462462931
2^64717+1 = 652025681383812779
2^64763+1 = 108565965025854923
2^64763+1 = 18478065862625992921
2^64763+1 = 4281593005798457
2^64811+1 = 168754174582369
2^64811+1 = 1780235517709999379
2^64817+1 = 105305802818231392844174713
2^64849+1 = 12405456423665771
2^64877+1 = 231252742551038627
2^64877+1 = 2577359216943468426289
2^64877+1 = 79456522445364631841
2^64879+1 = 219131940120644474392169
2^64919+1 = 506386771627614499285673
2^64969+1 = 2223286641153881
2^65027+1 = 148412698744643
2^65063+1 = 13756355917335947
2^65063+1 = 40533309198147131
2^65071+1 = 107391791142937011145160923
2^65089+1 = 21892547553332532043417
2^65099+1 = 24511258736809753
2^65101+1 = 7578013206027699953059
2^65129+1 = 10185675333209329
2^65129+1 = 1431319768421664041
2^65147+1 = 672755939180979179
2^65171+1 = 174443199126102307
2^65171+1 = 7623966613353028577
2^65173+1 = 8938353792972807132617
2^65203+1 = 23934991441044833
2^65213+1 = 2917940675706347
2^65239+1 = 3471188865563449921147
2^65269+1 = 121374380225706564793
2^65323+1 = 5554943036533769
2^65323+1 = 56355618237368545603
2^65353+1 = 31189339507228070606297
2^65371+1 = 21997117891193213011
2^65371+1 = 7696526328870419
2^65393+1 = 269965193927297123
2^65407+1 = 24156462490356737
2^65413+1 = 254878579091329
2^65413+1 = 437752871137969
2^65437+1 = 16778227002081896708603
2^65437+1 = 487368433453339
2^65519+1 = 157526450600489
2^65539+1 = 225395061638710121127997523
2^65551+1 = 113862705223017977
2^65557+1 = 3212038841346097457
2^65563+1 = 3154566333535446224209
2^65579+1 = 3465699427030799901289
2^65687+1 = 2737619893994008033
2^65699+1 = 30533108418903612707
2^65701+1 = 1908071388122833
2^65701+1 = 9722176130638555921
2^65713+1 = 55525336633325513
2^65717+1 = 1972661968855175385927761
2^65761+1 = 164901189994571
2^65777+1 = 44741042186681943689
2^65837+1 = 11628943726899175150883
2^65837+1 = 1177687273455841
2^65867+1 = 24093518471051083121
2^65867+1 = 70048947327183351383851
2^65881+1 = 988781880288489341291
2^65881+1 = 991992810726619217
2^65957+1 = 111659343744678451
2^65957+1 = 11775541942680641
2^65957+1 = 6883067490538912427291
2^65981+1 = 1541459101669123969
2^65981+1 = 56545795762813866885589739
2^65983+1 = 18136174557135499
2^65993+1 = 96580700943540129045083[/CODE]

 axn 2019-01-11 13:45

66k-70k
[CODE]2^66029+1 = 4682229387671684604187
2^66037+1 = 35517247369506232638683
2^66041+1 = 348438464152937
2^66047+1 = 179071539232518643
2^66067+1 = 479971537857187908923
2^66089+1 = 154776589108819
2^66107+1 = 558119515836894954836232523
2^66109+1 = 149950496615364560363
2^66137+1 = 12527674461124562399657
2^66161+1 = 2328308841001652387038915129
2^66169+1 = 97836117365181952764285307
2^66221+1 = 3144013238125282387
2^66301+1 = 105548443558976905464577
2^66347+1 = 187854267762745377248683
2^66361+1 = 15912574427040812136853670827
2^66361+1 = 4752670124621845180553
2^66361+1 = 841247640280067
2^66361+1 = 983920209032784017
2^66373+1 = 90007853404346531
2^66377+1 = 1802595732315467
2^66383+1 = 18771259608914243
2^66403+1 = 2109629947260867497
2^66431+1 = 3345047821173736059219923
2^66467+1 = 938465863118406377
2^66491+1 = 112545331226264752020299
2^66499+1 = 257750511013773899197073
2^66509+1 = 990401219296098900247916809
2^66541+1 = 1495150995199643
2^66569+1 = 28659589503877085521
2^66571+1 = 28771871363430955888246337
2^66571+1 = 486013112398731564436217
2^66601+1 = 127707655528777153
2^66617+1 = 4459193494437553
2^66653+1 = 15728635469167987959323
2^66653+1 = 381518611581353
2^66739+1 = 172420939219174797539
2^66749+1 = 3174123408633161220706411
2^66751+1 = 1301031772982307610841
2^66797+1 = 78365211217897340589001
2^66809+1 = 25471853005018482259
2^66821+1 = 173148573907340043091
2^66851+1 = 8302769164502137081
2^66883+1 = 37251400651329152459
2^66931+1 = 3323425053052361633339239104281802827
2^66931+1 = 76213325641162739
2^66959+1 = 211531659313336081
2^66959+1 = 823157503466088107
2^66977+1 = 141904123123034046097787
2^67021+1 = 15218086458139653121387
2^67021+1 = 2374941315543634934140771
2^67021+1 = 4556649273753174337
2^67043+1 = 96718010377702277481419
2^67049+1 = 3535792083935832049794827
2^67129+1 = 35299666869673188913897
2^67139+1 = 264031237859507
2^67157+1 = 2545112724956308205826923
2^67181+1 = 191567786274789520570001383217
2^67181+1 = 315304912052569874795321497
2^67189+1 = 498963641473444920659
2^67217+1 = 191096343709374513259
2^67261+1 = 7500260470921144912009
2^67273+1 = 11109877147035079409
2^67273+1 = 12786526706312420973739
2^67339+1 = 75226525152346126921
2^67349+1 = 7674755395215313
2^67391+1 = 98638952687598091
2^67399+1 = 3351222406965187
2^67399+1 = 8879670131493024133175657
2^67429+1 = 52786862383461730339
2^67453+1 = 27658107567464468363281
2^67453+1 = 806195192162919883
2^67477+1 = 6115886865496657
2^67481+1 = 35352536619331621181587
2^67481+1 = 7982706522180866081149633
2^67489+1 = 143322134297030869489
2^67489+1 = 399767591357443165431307
2^67489+1 = 85876801863530368527761
2^67499+1 = 440713272070331866147
2^67537+1 = 12077109739922588899337
2^67537+1 = 1794431197403203763
2^67547+1 = 1057823669930330987
2^67547+1 = 165027455432923067
2^67559+1 = 3757752421392718981952939
2^67579+1 = 395006832190443194489
2^67589+1 = 28125214088228219555953
2^67601+1 = 84710224755148644858270899
2^67607+1 = 23606129668968272291
2^67651+1 = 140042743586095312333932698323
2^67679+1 = 110496492499384723
2^67733+1 = 16991969657848707538771
2^67757+1 = 1547902431170119918163
2^67759+1 = 3691743741330262150335091
2^67763+1 = 267486530747742713238005443
2^67829+1 = 4747853787789189529
2^67853+1 = 1950251814680685008249
2^67853+1 = 3002577996005165899
2^67883+1 = 389685622427711777
2^67901+1 = 167913890504273377
2^67927+1 = 13143780749388635751499
2^67931+1 = 739382026252785353
2^67939+1 = 8157446235974768796473
2^67943+1 = 221983066119994476491960867
2^67961+1 = 166557299327963
2^67961+1 = 83670937404870624859
2^67979+1 = 519531720469087203432607603
2^67979+1 = 69988934314981296707
2^67987+1 = 3849030004622719547
2^67993+1 = 158334727151926117099
2^67993+1 = 892819458308507
2^68023+1 = 180212008267777
2^68023+1 = 795280454454108769
2^68053+1 = 1183297602887849
2^68071+1 = 4898012655892680871721
2^68141+1 = 110545591670332043
2^68161+1 = 580057676552611
2^68213+1 = 7689166188642383572177
2^68279+1 = 4079733179203793
2^68311+1 = 1628153211407223289
2^68311+1 = 2735097071107481
2^68329+1 = 156735660208301925985498081
2^68351+1 = 30758436849203994299
2^68371+1 = 159216858574858387
2^68437+1 = 27498268649021207708507
2^68449+1 = 55998638924393723
2^68449+1 = 86874075238293154547
2^68477+1 = 412652114788709142961283
2^68483+1 = 5652921209437764621005947
2^68483+1 = 974016239808497
2^68491+1 = 51285160191293183714843
2^68501+1 = 1538786629719922650472081
2^68507+1 = 70588460413492269914593
2^68531+1 = 2177413703745136135360051
2^68531+1 = 786865741704958313
2^68543+1 = 6011537703826281624419
2^68567+1 = 73484844170042713
2^68567+1 = 90193429887166257601
2^68597+1 = 279249912101850598408547
2^68611+1 = 3194904433269516051659
2^68683+1 = 21923008713344797603
2^68687+1 = 506901826764059
2^68711+1 = 133637581215474064092174289
2^68713+1 = 176294669241831638259698389682729
2^68729+1 = 163068574143457
2^68743+1 = 397249206958552363
2^68749+1 = 110616278627541027308249
2^68771+1 = 25210324699478772906053033
2^68777+1 = 2529985912591769267
2^68813+1 = 2688694569113449745604491
2^68821+1 = 18778712075563900045624403
2^68891+1 = 126257308593089153
2^68891+1 = 25680074084892672746683
2^68897+1 = 1393743511847347083889
2^68917+1 = 3549372970829097299
2^68993+1 = 140464914810879283
2^68993+1 = 7108015059251218210531
2^69029+1 = 12969505272600013978793
2^69031+1 = 232868144767171
2^69031+1 = 77663942411966463821603
2^69061+1 = 10568018443460280617
2^69119+1 = 180754642953793
2^69143+1 = 11091129295927541881
2^69197+1 = 303707507816658224603
2^69239+1 = 127013769164110489
2^69257+1 = 35697650773175059187059
2^69259+1 = 47101939684803725779
2^69371+1 = 8652743650055703272923
2^69379+1 = 31988049702673777
2^69379+1 = 469680559861807567171
2^69389+1 = 2203018766133914891
2^69431+1 = 744365146855750931115089
2^69467+1 = 2493902245351333716986335939
2^69497+1 = 32655916814200145971
2^69593+1 = 47620670021624028958033
2^69623+1 = 42331276981729361155121
2^69691+1 = 207438238956982404490313
2^69737+1 = 12882828524691526201
2^69779+1 = 1870811869941369587
2^69779+1 = 5067233861608832923
2^69809+1 = 2584229926382101099
2^69833+1 = 167340523560282197903989241
2^69833+1 = 194138375888823573430603
2^69847+1 = 1915922439158489
2^69857+1 = 480196463614849
2^69899+1 = 7471577301522497
2^69941+1 = 9215690152724147[/CODE]

 axn 2019-01-12 12:04

[CODE]ECM found a factor in curve #14, stage #2
Sigma=5431437631844099, B1=50000, B2=5000000.
2^70921+1 has a factor: 13578077394426643146204578472443260177 (ECM curve 14, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
So, (2^70921+1)/3 = 709211 · 129478105736831177 · 104867748235555477001 · PRP21306

PS:- The factor reported by ECM is a composite

 paulunderwood 2019-01-12 13:24

[QUOTE=axn;505688][CODE]ECM found a factor in curve #14, stage #2
Sigma=5431437631844099, B1=50000, B2=5000000.
2^70921+1 has a factor: 13578077394426643146204578472443260177 (ECM curve 14, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
So, (2^70921+1)/3 = 709211 · 129478105736831177 · 104867748235555477001 · PRP21306

PS:- The factor reported by ECM is a composite[/QUOTE]

Congrats :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^70921+1)/3/709211/129478105736831177/104867748235555477001" | ../../coding/gwnum/bpsw-2 - 1 2 70921 1

Testing (2*x)^((n + 1)/2) == -2 (mod n, x^2 - 3*x + 1)...
Likely prime!

real 0m3.769s
user 0m3.516s
sys 0m0.016s
[/CODE]

 axn 2019-01-14 13:17

70k-73k
[CODE]2^70003+1 = 5110266574145624579
2^70003+1 = 896833597678441
2^70111+1 = 1180265491056153936403
2^70117+1 = 279482962403759227
2^70117+1 = 33697723113682299015667
2^70141+1 = 299920138022180084729
2^70163+1 = 34265526228873047975057
2^70199+1 = 454502016890176969530521
2^70199+1 = 49318840482668174837633
2^70201+1 = 1356380561692620132139
2^70201+1 = 274666288129809143003851
2^70223+1 = 17439460601328553
2^70223+1 = 345951733956347016881
2^70229+1 = 1122725706073873275211
2^70229+1 = 82974590956195573891
2^70241+1 = 372156790439028011
2^70351+1 = 33857867791342161907
2^70351+1 = 6313353520916681
2^70381+1 = 2623271369586713166333135923
2^70393+1 = 124534404738285233
2^70423+1 = 12950742357330156779297
2^70457+1 = 3248436254405817179
2^70459+1 = 8607763141812137243
2^70481+1 = 146296386890819022521
2^70481+1 = 47513531674629646609184339
2^70487+1 = 201951054670361
2^70501+1 = 115053424405002649
2^70507+1 = 164095487410985669865040129
2^70583+1 = 600367677288334195531
2^70607+1 = 17544336851287339
2^70619+1 = 2125274911179677915401
2^70621+1 = 253527958372359179
2^70621+1 = 261223712920657
2^70657+1 = 17942521611575921
2^70667+1 = 12471891539165590369
2^70667+1 = 43620197649453493095317777
2^70729+1 = 792507477401557768441
2^70783+1 = 23133490082570399236897
2^70849+1 = 937276909663855511848091
2^70853+1 = 5247516826380259
2^70853+1 = 5589615521866348204201
2^70877+1 = 4142709565684654312428257
2^70877+1 = 434570644338177161
2^70913+1 = 1461660300086325289
2^70921+1 = 13578077394426643146204578472443260177
2^70949+1 = 299790695348406931
2^70957+1 = 195635973691337591473571
2^70981+1 = 1583483522335190332913159321
2^70991+1 = 117971152953070837605817
2^70991+1 = 412135661577325348380649
2^71059+1 = 1046308058952890578507566667
2^71081+1 = 364388650710881779
2^71119+1 = 2024933178452803
2^71129+1 = 52258292927304131
2^71167+1 = 606762071556990985774387
2^71233+1 = 1760756218696103094807580417
2^71237+1 = 21562888098741823259
2^71249+1 = 5238253785754748459
2^71261+1 = 956184186639516639169
2^71327+1 = 67999951599326509953894183611
2^71347+1 = 111436417539984836617
2^71347+1 = 1852768715143880838903593
2^71353+1 = 194561717972057
2^71363+1 = 2062972674205001889817043
2^71363+1 = 38047024220326260912601393
2^71363+1 = 432790354967627
2^71413+1 = 2531267927269649
2^71437+1 = 24828554134715899
2^71443+1 = 2504832025843704123617
2^71453+1 = 31456192453120459
2^71453+1 = 54401658810924863088753057961
2^71453+1 = 6536672669330347
2^71471+1 = 109736176273241764412836723
2^71483+1 = 427328601108763816892269318070777
2^71483+1 = 43352540152513507
2^71483+1 = 4913459061310932547
2^71483+1 = 611081402392866239617
2^71503+1 = 250926406039829297
2^71537+1 = 2621587179238278483451
2^71551+1 = 3394508798280572059
2^71551+1 = 846610284415449136956577
2^71647+1 = 647246821748110579
2^71671+1 = 59134417185815036189584153
2^71699+1 = 1958362413057558964307
2^71707+1 = 31321732322514687536321
2^71711+1 = 1231310045832018304615193
2^71713+1 = 195549002915156967611
2^71761+1 = 102369072930096857
2^71777+1 = 2235471590044716239683
2^71807+1 = 5266102833304163
2^71809+1 = 557176123704903291923
2^71837+1 = 553028632342821653611
2^71849+1 = 10670822413993662017
2^71879+1 = 21624413594886763
2^71947+1 = 7515003631085677496846603
2^71983+1 = 869405898791747
2^71987+1 = 8136522786923024427622907
2^71993+1 = 539246385293887840422209
2^71999+1 = 885844882155977
2^72043+1 = 11498443469470316987
2^72073+1 = 307536648204089
2^72089+1 = 6336180428700643
2^72103+1 = 28901614505533513
2^72109+1 = 50722096171331757929
2^72139+1 = 35349785307081481
2^72139+1 = 38884775442774831553723
2^72221+1 = 3757771798143403283
2^72221+1 = 611690817309260113
2^72223+1 = 27183069556563474074123
2^72227+1 = 336078011641543919483
2^72227+1 = 6698838106224427
2^72229+1 = 1016468213982462915041
2^72251+1 = 1846533104027881
2^72277+1 = 2488874425226656590049
2^72313+1 = 1785663146154428449
2^72337+1 = 15728751065904792259512001
2^72367+1 = 1874246984965954120993
2^72383+1 = 32115583242648211807706441
2^72461+1 = 1172213083980455947
2^72493+1 = 1701943071966839443412171
2^72533+1 = 21406792788460907237472553
2^72559+1 = 58812153140666978258483
2^72617+1 = 11785689510923688793
2^72617+1 = 155274779458291
2^72649+1 = 1106905124697532130939
2^72649+1 = 8760528364895783137
2^72671+1 = 86956083911279289420907
2^72679+1 = 1607798507389806280609
2^72689+1 = 341016471336907
2^72689+1 = 811173151724064326699
2^72707+1 = 5869655240511338236320457
2^72707+1 = 9097043404408389337
2^72727+1 = 784123789581946721923
2^72733+1 = 31597502204232857
2^72797+1 = 119585467281987011
2^72823+1 = 7596437583989843
2^72883+1 = 528474900096225059
2^72911+1 = 1306712102806668202179697
2^72911+1 = 143026408339351921822882537
2^72937+1 = 2005299432309097627
2^72949+1 = 7149290644421848787
2^72973+1 = 26725075783343730286405489
2^72977+1 = 678919391705969
2^72997+1 = 297192530908379
2^72997+1 = 8638053444521113[/CODE]

EDIT:- 111111111111[sub]2[/sub] Posts

 axn 2019-01-18 10:59

9.5k-10k to t35
[CODE]2^9859+1 has a factor: 118432065885251221169878802850525217 (ECM curve 1465, B1=1000000, B2=100000000)
2^9839+1 has a factor: 66232443181564293418304837041670731 (ECM curve 51, B1=1000000, B2=100000000)
2^9733+1 has a factor: 24245867458607381298459625015740649 (ECM curve 237, B1=1000000, B2=100000000)
2^9601+1 has a factor: 1397641732031634847364462497989124760089 (ECM curve 760, B1=1000000, B2=100000000)
[/CODE]

 axn 2019-01-18 14:06

73k-77k
[CODE]2^73013+1 = 79132934330362862367643
2^73039+1 = 301735367873813610274190291
2^73039+1 = 94297306689939299
2^73043+1 = 60705459947534288548729811
2^73063+1 = 1026231921453259
2^73079+1 = 409508287909214881
2^73091+1 = 3589412028044587267620793
2^73133+1 = 2928671710986750091889
2^73189+1 = 638632878431340697
2^73237+1 = 162017421445403
2^73237+1 = 4085342838871586150579659
2^73237+1 = 550603037703481389619
2^73243+1 = 140731194993415767043
2^73259+1 = 156748305785746518557489
2^73259+1 = 5366311871861526889
2^73277+1 = 1315202865009673
2^73303+1 = 17044566232943116937297
2^73327+1 = 8822822173986234163
2^73331+1 = 18492182944147394123
2^73369+1 = 6244878817017378667177
2^73379+1 = 30355074291690004654804459
2^73459+1 = 45769529884204142325394457
2^73471+1 = 2957571384125179524703577
2^73477+1 = 14872162528640191531
2^73483+1 = 293166934831787
2^73483+1 = 737751895220704099470803
2^73483+1 = 8766837096069643
2^73517+1 = 40694129782945841
2^73523+1 = 2343063889216907
2^73613+1 = 1258229559416833
2^73643+1 = 3392788279742651828993643907
2^73651+1 = 1070813241044806102138619
2^73673+1 = 204704548887889777
2^73673+1 = 382767897040684137900672137
2^73673+1 = 82668824231441590967821019
2^73721+1 = 7314519633133534832267
2^73771+1 = 1076489957098156064323
2^73819+1 = 952534357902899
2^73823+1 = 111789850932720689013281
2^73877+1 = 130155909718749793
2^73897+1 = 21500492417431109129
2^73907+1 = 1651838058824483
2^73907+1 = 227378203480859
2^73943+1 = 432083942408826157523
2^73961+1 = 107919861908528242871165963
2^74093+1 = 5608392579469192651
2^74099+1 = 4601780605934710077097
2^74159+1 = 545572295657371
2^74177+1 = 49515996177379694891
2^74209+1 = 4824480258236230729
2^74219+1 = 5088745335642023838266513
2^74231+1 = 3243567232683642208734799873
2^74257+1 = 116765041156724497
2^74287+1 = 173479118490939099649
2^74287+1 = 2837173640041805937097
2^74287+1 = 3023130876815243374305240569
2^74287+1 = 8267597616280881889
2^74311+1 = 1033180702322837879072683
2^74311+1 = 501723262682354329
2^74323+1 = 14379544033849422028987753
2^74357+1 = 1988482829627473
2^74377+1 = 1169989674436201
2^74381+1 = 560334809228613997913
2^74383+1 = 1404959897196781360697
2^74441+1 = 12907649270527965769
2^74449+1 = 5208548489322739361
2^74471+1 = 401398467033827
2^74471+1 = 4682164492143082309873
2^74509+1 = 115123013222433323
2^74521+1 = 259321009640024443
2^74551+1 = 2989750645321393
2^74611+1 = 219742470279307
2^74707+1 = 17279203756192409
2^74717+1 = 8502774645164041657
2^74731+1 = 105788197806830113
2^74747+1 = 271222782120635026587497
2^74761+1 = 1442260637438650027
2^74779+1 = 26238212228997787553
2^74797+1 = 24804741850965776960634299
2^74827+1 = 9041187338666472097
2^74831+1 = 23546127863481121
2^74873+1 = 3517555866180408329
2^74873+1 = 5047886189873465563
2^74897+1 = 78509082942241471939
2^74929+1 = 44377702004269823977
2^74933+1 = 368366587354026434689
2^74941+1 = 104067872400298430321
2^75013+1 = 35494597679754416628419
2^75017+1 = 3235995343593308161
2^75037+1 = 17472078576583480971697
2^75041+1 = 269604191448114203
2^75041+1 = 68350772979490259
2^75079+1 = 330788193603601
2^75109+1 = 5121868175008350979651
2^75161+1 = 7437960303753002478063281
2^75181+1 = 974748817272979667603
2^75211+1 = 5125147230172556560059714307
2^75211+1 = 69458583297168467723
2^75217+1 = 23602155060302826809
2^75239+1 = 2562885294594613236311235131
2^75253+1 = 114669879003819043
2^75277+1 = 430235232527108147281
2^75277+1 = 473928155555228793950433083
2^75307+1 = 2531493859451616535303363
2^75307+1 = 3022514790059658194006987
2^75307+1 = 794109707582717282753
2^75323+1 = 16632974051748611873474539
2^75347+1 = 106727676917598265413097
2^75353+1 = 521797139884291
2^75367+1 = 143460045589315057999657
2^75367+1 = 350896521049487068043
2^75377+1 = 394219379603059897
2^75391+1 = 40521894854813854413978503136357131
2^75391+1 = 412041551622913
2^75431+1 = 2137158917667793
2^75503+1 = 30376947630089603923
2^75533+1 = 7506297397271681
2^75541+1 = 15674815153964253643104347
2^75541+1 = 2322648844473896132436691
2^75541+1 = 62202979582676227
2^75617+1 = 1470461710183769
2^75617+1 = 52828763205221284849
2^75629+1 = 3188965106888773609
2^75653+1 = 21842856985895067132793
2^75659+1 = 1976884740654049
2^75683+1 = 2395575412466129
2^75707+1 = 4636133982628721
2^75709+1 = 147829054573697848801
2^75709+1 = 909642088806994454801
2^75731+1 = 2667143256737878889
2^75767+1 = 127623153348386747
2^75781+1 = 1693215276359705617
2^75787+1 = 1176951001653187
2^75787+1 = 299319132876660288323
2^75787+1 = 978801328064625869123
2^75793+1 = 492519534670011073
2^75797+1 = 379077918537746138443
2^75853+1 = 16199866340941819
2^75869+1 = 14605389013780657
2^75931+1 = 58051766815117126123
2^75937+1 = 1209525119803657
2^75967+1 = 88901427493945723
2^75983+1 = 8071354611945065041
2^75989+1 = 44197093491514628297
2^75997+1 = 75040201669334936809
2^76003+1 = 58814812160858179
2^76003+1 = 8125139264785643
2^76039+1 = 443765278530859
2^76039+1 = 723654085865882015907077998849
2^76123+1 = 414371774044986770131267
2^76129+1 = 703727282205187
2^76147+1 = 2718177762513859492143667
2^76157+1 = 25924592679168244580454059
2^76159+1 = 104609599066735027
2^76231+1 = 14303249589937005433
2^76253+1 = 920478460933131356251
2^76259+1 = 1034441989866210281
2^76261+1 = 160889083902916106456377
2^76289+1 = 259207920027726251
2^76303+1 = 4030461401299313
2^76333+1 = 226040978213306338947733005073
2^76367+1 = 2674077812837551255120275449
2^76423+1 = 15889552175513297
2^76519+1 = 17865851193100499
2^76519+1 = 960149330959169441
2^76541+1 = 6280956320301495920434211
2^76579+1 = 65799420417129475318849
2^76607+1 = 245411117968760083
2^76607+1 = 40340770839442193123
2^76673+1 = 15655705645706298862771
2^76679+1 = 4274672207517882041
2^76753+1 = 33638809004646777097
2^76771+1 = 51541629641185763
2^76777+1 = 246918282665489
2^76829+1 = 108481575047531771
2^76831+1 = 1472269363517131385200793
2^76847+1 = 1707289762491596210459040609575633
2^76871+1 = 284324776800457
2^76871+1 = 38562173376027017
2^76883+1 = 4045278481573510081
2^76913+1 = 183388410563906057
2^76913+1 = 191080368422947
2^76949+1 = 25711422403093334657
2^76961+1 = 105826524835221277477627[/CODE]

 axn 2019-01-21 13:13

77k-80k
[CODE]2^77017+1 = 75201095702495899582009
2^77029+1 = 723271121687422709867
2^77047+1 = 29284448969295011
2^77069+1 = 2745437972834930507
2^77101+1 = 180553328122337
2^77141+1 = 6246393823236266860889
2^77167+1 = 930269057845820956729
2^77201+1 = 114695057907656593
2^77237+1 = 18272934213252422947
2^77237+1 = 347957238400554468712155557713
2^77243+1 = 46214164015275557699
2^77243+1 = 820471936862323
2^77249+1 = 31851830339522940750855689
2^77279+1 = 7141504255166877601
2^77317+1 = 19730405058902273041
2^77323+1 = 497936123186141993
2^77347+1 = 4506706336169150374041329
2^77351+1 = 28888573732326030020483
2^77359+1 = 400436385336941989201
2^77377+1 = 2763893457087350733883
2^77417+1 = 89931592131615237571
2^77419+1 = 4426396638502734881987
2^77431+1 = 152866546415742719897
2^77447+1 = 219642305078307034907
2^77477+1 = 21595211728919230699481
2^77479+1 = 37152399395421765640231747
2^77479+1 = 3804927106743737682299253161
2^77489+1 = 35938452047922836473
2^77491+1 = 202485465164002739
2^77513+1 = 257922246755843
2^77521+1 = 57553318892834589576833
2^77551+1 = 20258477262452933363
2^77617+1 = 4851415389643999513
2^77617+1 = 5938214297207794387
2^77641+1 = 8644530098730577633
2^77659+1 = 91549850876728193
2^77681+1 = 133449034239334998003619
2^77687+1 = 149154923697593491
2^77687+1 = 21523044262187529842617
2^77711+1 = 59952127529820765435303924211
2^77713+1 = 11214523523663059
2^77731+1 = 512290150934807491
2^77743+1 = 5562992346818743547
2^77743+1 = 65204029110880267
2^77773+1 = 11569845626561483
2^77797+1 = 9961358940315774809
2^77801+1 = 351294802392234749685137
2^77839+1 = 226274598359179355963
2^77863+1 = 77780582378784692843
2^77863+1 = 942249883618553
2^77867+1 = 2735829844110907033159651
2^77867+1 = 523732188680326663566827
2^77867+1 = 5477835016311486011
2^77893+1 = 4074338094088651
2^77899+1 = 75681711529828152199531
2^77929+1 = 523065684361061108194484353
2^77951+1 = 1141934560969617593081
2^77951+1 = 2838051216259991569
2^77969+1 = 1031350513372283891
2^77983+1 = 14121013599477171857
2^77999+1 = 151787180411915922545051
2^78017+1 = 3347151052873215089
2^78101+1 = 10750596560827254315497
2^78121+1 = 58020145433786547353
2^78137+1 = 113909357927655399203
2^78157+1 = 853856599976730665201
2^78167+1 = 10073268600129695899
2^78167+1 = 1106605390624411
2^78179+1 = 46904640488138591265459838403
2^78179+1 = 7383814873976919241
2^78203+1 = 20318621791512259
2^78277+1 = 14531046460721150179
2^78301+1 = 38140250060962735044863249
2^78307+1 = 463578354929862364548451
2^78311+1 = 482040652498815131824649
2^78317+1 = 1487605481314280443
2^78367+1 = 7984682552248382600611
2^78497+1 = 2653857162199057
2^78497+1 = 287928176907557571083
2^78509+1 = 16574256611948685961889
2^78509+1 = 46886845942450641001139
2^78511+1 = 4404798297628765006681
2^78517+1 = 85811774465571035969
2^78539+1 = 22392100873016947
2^78539+1 = 77496200290639228409
2^78569+1 = 1772636833434052701497
2^78571+1 = 20239979775257559147283
2^78571+1 = 35827453137057288540851
2^78577+1 = 181734547208821659707
2^78623+1 = 3391201640510780421443
2^78697+1 = 40289059421512098289
2^78697+1 = 9289835725481918393
2^78707+1 = 22825456406663723
2^78707+1 = 25079696678450803187
2^78713+1 = 128594773293444439243
2^78737+1 = 1189663900139969297
2^78779+1 = 2133884666530654642155371
2^78779+1 = 87249758707602212910449
2^78781+1 = 4120693647457405607273
2^78787+1 = 2235135568600027
2^78809+1 = 930151015756420469651
2^78877+1 = 1069920354462947033
2^78901+1 = 537974594246822203
2^78919+1 = 1164811294020001
2^78919+1 = 20727778300062102833
2^78919+1 = 3328135201304827
2^78977+1 = 26976971863025083
2^78977+1 = 566417375078958017
2^78979+1 = 1554077912150513
2^78979+1 = 220766113331885993
2^78979+1 = 31272742501543219
2^79039+1 = 999594469391947560707
2^79063+1 = 55868111715424651849
2^79111+1 = 629982308460828731
2^79147+1 = 233789352526694347
2^79153+1 = 2630703304512699209
2^79153+1 = 42809675506647824683
2^79181+1 = 1157892854511031828648671907
2^79193+1 = 132004063172165144531
2^79193+1 = 80314193306182606066217
2^79229+1 = 1127439210150787
2^79229+1 = 388054828419321360931
2^79259+1 = 24051888286846925280361
2^79259+1 = 2419708873523070116627
2^79273+1 = 80377078902996245575241
2^79283+1 = 676691551917373463777
2^79301+1 = 156699851200897428667081
2^79301+1 = 1752091452640465769369
2^79309+1 = 18171546791047849049
2^79349+1 = 16979053052160452775337
2^79349+1 = 748758016087852504297
2^79357+1 = 284715223626554853790267
2^79393+1 = 24683015794831360157057
2^79393+1 = 8421029517547650323641
2^79397+1 = 2408837998444603250337179
2^79433+1 = 837301673865232697123686009
2^79481+1 = 1491941617997137671288521
2^79531+1 = 1684672193334299939048281
2^79589+1 = 197809692134939
2^79589+1 = 396616894695907
2^79633+1 = 360632288436361
2^79657+1 = 1499961822155443
2^79697+1 = 13204307626682891449
2^79697+1 = 253451228851996338217
2^79757+1 = 1436165598376211
2^79757+1 = 23222550683574173983691
2^79843+1 = 26385984840322273633
2^79847+1 = 525917112756598578715099
2^79867+1 = 8004559316458318863230326867
2^79967+1 = 26696339269894494913
2^79973+1 = 507828487779120556553
2^79997+1 = 15458872893788155532707
2^79997+1 = 18780646913209319507[/CODE]

 axn 2019-01-26 01:47

80k-83k
[CODE]2^80071+1 = 2120000408626395047552147
2^80071+1 = 8868157757543681
2^80077+1 = 585953812635361
2^80077+1 = 8081354742226391641
2^80107+1 = 9698974791402251
2^80111+1 = 1544923545679021171
2^80111+1 = 19276030579171445257
2^80141+1 = 27499541636800676181281
2^80147+1 = 130853593797091597769
2^80167+1 = 493030006509482072865763
2^80191+1 = 6898453962766208746451
2^80233+1 = 2225910609218266291
2^80233+1 = 430598244978961
2^80251+1 = 2945083307737203851
2^80309+1 = 135421022499379
2^80309+1 = 650935270164089
2^80317+1 = 120410646761149067
2^80329+1 = 13285894034586870419
2^80329+1 = 1414245877800667
2^80347+1 = 2380550630843656976083
2^80363+1 = 689498105445049
2^80387+1 = 810617672675768829896005721
2^80449+1 = 144226500991976965925801
2^80473+1 = 1625205288726987937
2^80491+1 = 15754641362069187870665161
2^80491+1 = 85123325245555439681
2^80491+1 = 914212786486533505529
2^80513+1 = 46003721425351125443042181500987
2^80527+1 = 13953487408857041
2^80557+1 = 149850227696850539699
2^80557+1 = 5640253785788606339991803
2^80567+1 = 26582882730641970447811
2^80621+1 = 2270579767368499
2^80629+1 = 1266094585138459799939
2^80669+1 = 1214308536934192400849
2^80669+1 = 24049792529450137
2^80669+1 = 6262740992523623576489
2^80677+1 = 95047911127774883
2^80713+1 = 22140734091241927801
2^80747+1 = 6312401899106267
2^80761+1 = 1006721671354789607081
2^80761+1 = 410108805623662124411
2^80789+1 = 2958049627454087932523
2^80803+1 = 3758852898768502237403
2^80833+1 = 160319494824639449190779
2^80833+1 = 549954154697300479219777
2^80849+1 = 41584741356592038928867729
2^80917+1 = 11381610388067954369
2^80929+1 = 333823597222515329
2^80963+1 = 117696713607574939
2^81017+1 = 7574237435887151387
2^81019+1 = 4150600351394099
2^81041+1 = 143427795466067697289
2^81047+1 = 1306252713016499
2^81077+1 = 5452638392326465987
2^81077+1 = 8217486011150927617
2^81131+1 = 328236540207601577
2^81163+1 = 191114163637498051
2^81181+1 = 297078563160233
2^81181+1 = 334857580894985723
2^81181+1 = 52322720489844262023481
2^81181+1 = 870404357824681
2^81223+1 = 357457040130142171749300403
2^81233+1 = 3537795768440519657
2^81283+1 = 1709025401746603121
2^81283+1 = 2077572582199711459
2^81343+1 = 9023231900214647833747
2^81371+1 = 1434230553586830567308704993
2^81371+1 = 497817599733690011
2^81401+1 = 2050614770735252201
2^81401+1 = 72031788041267081764408561
2^81409+1 = 67409591986077284987
2^81463+1 = 90954631911919966643
2^81509+1 = 361420019327161644881
2^81517+1 = 1963597398947788066136339
2^81517+1 = 243412332236837653324771547
2^81547+1 = 124827442411898476734686401
2^81547+1 = 66058567420400791931
2^81553+1 = 2661130501726121
2^81563+1 = 68473849823139950513
2^81611+1 = 4240767464917941754070491771483
2^81629+1 = 484456429381182436153
2^81637+1 = 283305196771923734307617
2^81649+1 = 1950290879802451
2^81649+1 = 3827697466549337
2^81649+1 = 81685810543415436890689
2^81689+1 = 1060904982552370171
2^81701+1 = 105423977585341691
2^81701+1 = 189809634665175891131
2^81769+1 = 331735624278142479283649
2^81773+1 = 223477519815092390469931
2^81799+1 = 5983159293773585701297603
2^81839+1 = 2932887333382817
2^81847+1 = 188942633998721
2^81853+1 = 10810101668025523
2^81869+1 = 20406930547247466060259
2^81901+1 = 300894702760754949059
2^81919+1 = 2790986493958307879510803
2^81919+1 = 28802771787050252643161
2^81929+1 = 1021639674175719835942099
2^81953+1 = 194964221451213139
2^81953+1 = 8290104065664977
2^81971+1 = 16833322650299699
2^81973+1 = 375456628251564601846890001
2^82007+1 = 4275665018544664067
2^82009+1 = 4434141163408886054337697
2^82021+1 = 2208676171049190331
2^82067+1 = 23838523065963585082241
2^82067+1 = 30114929455697683
2^82129+1 = 3463570516278155993
2^82163+1 = 155597690593512257
2^82171+1 = 67028719643789761657941577
2^82207+1 = 501803325531966560723
2^82237+1 = 1760713595320849177
2^82267+1 = 182845915041066551051
2^82267+1 = 18511302131000444108899
2^82339+1 = 174234873648601
2^82339+1 = 495033352181025923
2^82349+1 = 11886827202960020644331
2^82483+1 = 15685389821332111860323
2^82483+1 = 593875233649021735009
2^82549+1 = 509352060176034575087227
2^82559+1 = 20896735807713609271843
2^82561+1 = 120886619536809378740843
2^82601+1 = 210203975011311893641
2^82613+1 = 504143130394983029722417
2^82619+1 = 466341427569229784396257
2^82619+1 = 632813025965277624109691
2^82633+1 = 2316122660197877929
2^82651+1 = 14378500291729033643
2^82657+1 = 6211441397566033
2^82727+1 = 2904936754283075569
2^82757+1 = 1643869916426043967623203
2^82811+1 = 1415932604096726570083
2^82813+1 = 1247998903643994022577339
2^82837+1 = 146503293032507
2^82883+1 = 5103610654878427
2^82997+1 = 28925131026789127916147
2^82997+1 = 53258672391028895377[/CODE]
And ...
[CODE]ECM found a factor in curve #208, stage #1
Sigma=4163419390201143, B1=50000, B2=5000000.
2^85331+1 has a factor: 429734853667011523504561 (ECM curve 208, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
So (2^85331+1)/3 = 335862817 · 429734853667011523504561 · PRP25655

 paulunderwood 2019-01-26 02:05

[QUOTE=axn;506871]
And ...
[CODE]ECM found a factor in curve #208, stage #1
Sigma=4163419390201143, B1=50000, B2=5000000.
2^85331+1 has a factor: 429734853667011523504561 (ECM curve 208, B1=50000, B2=5000000)
Cofactor is a probable prime!
[/CODE]
So (2^85331+1)/3 = 335862817 · 429734853667011523504561 · PRP25655[/QUOTE]

Congrats :toot:

[CODE]ime ./pfgw64 -k -f0 -od -q"(2^85331+1)/3/335862817/429734853667011523504561" | ../../coding/gwnum/bpsw-2 - 1 2 85331 1

Testing (2*x)^((n + 1)/2) == 2 (mod n, x^2 - 6*x + 1)...
Likely prime!

real 0m4.603s
user 0m4.764s
sys 0m0.008s
[/CODE]

 axn 2019-01-26 10:51

83k-86k
[CODE]2^83003+1 = 3161816170421641
2^83003+1 = 975600455552561
2^83009+1 = 450592220403208897573633
2^83071+1 = 45800085063850511299
2^83101+1 = 2131678394222270123
2^83137+1 = 1690983774186883698001
2^83231+1 = 274784844624975107139097
2^83233+1 = 21430564968957326284217
2^83233+1 = 496487097724616707
2^83243+1 = 338464426904988841
2^83257+1 = 76771712838933382162619
2^83267+1 = 25273090999306043867
2^83269+1 = 1524837388921283447024348449
2^83299+1 = 105742890903092210529026899211
2^83299+1 = 229147835393500582598713433
2^83357+1 = 131562639567815260747
2^83399+1 = 1979068636538400289
2^83399+1 = 6884525932858494451
2^83407+1 = 2252530386066259346491
2^83431+1 = 1206011522333451283369
2^83437+1 = 100103611098394957248289
2^83449+1 = 9771274573243187
2^83471+1 = 99268263196452350165657
2^83497+1 = 7571110247474819087297
2^83557+1 = 1462807414046557841
2^83557+1 = 477056904124705286808731
2^83561+1 = 97661469063658990754393
2^83591+1 = 189742497921432331
2^83639+1 = 3983375420177563
2^83639+1 = 5422582616966336293467571
2^83717+1 = 1268430454938575540377
2^83717+1 = 44875958325580027
2^83777+1 = 91571192035423776953
2^83813+1 = 36316488487648356316123
2^83833+1 = 5459474707096777
2^83857+1 = 20726017390686548795051
2^83903+1 = 96996035973482689
2^84011+1 = 3019317251460956203
2^84017+1 = 1740574457558474604215537
2^84017+1 = 182389027878210467
2^84053+1 = 2502372060889417
2^84089+1 = 11334862313412654658529
2^84143+1 = 54123189060187008502723
2^84179+1 = 224144972193601
2^84181+1 = 215637574145713
2^84191+1 = 66562304249534857
2^84211+1 = 6317535133186602961
2^84229+1 = 32937083327750597586997081502970091537
2^84239+1 = 99405182186038601099
2^84247+1 = 1874361939984419
2^84307+1 = 5304854770705686409
2^84313+1 = 2150646526038419
2^84349+1 = 4942674223543019891
2^84391+1 = 8210755202676491
2^84401+1 = 104054361480129409
2^84421+1 = 277937197017923959273
2^84443+1 = 39958050818036177
2^84457+1 = 9934713033273735313
2^84509+1 = 16774282168778587
2^84521+1 = 1986064239240449270560753
2^84533+1 = 242996851375786307554561
2^84629+1 = 3950907802223511450523
2^84691+1 = 2697922711261229147411
2^84713+1 = 20902541077701445313
2^84731+1 = 4580453764013798851
2^84787+1 = 4447602916244011
2^84787+1 = 7683037012272223697
2^84809+1 = 10919822432541996299
2^84809+1 = 5179757653191971657122811
2^84811+1 = 316746156762079034697827
2^84811+1 = 48137389748869829892360889
2^84857+1 = 12224801062112106326689
2^84859+1 = 6476143021189661006309891
2^84869+1 = 1999600699468891
2^84871+1 = 13825393357170827
2^84919+1 = 4026471860563408603187
2^84977+1 = 49167611327004494099
2^85087+1 = 120379222415857002707459358639881
2^85109+1 = 11478613170288809
2^85121+1 = 1168565767422473579
2^85147+1 = 346816042466717017
2^85193+1 = 1304001076230594365593
2^85201+1 = 390034280028647847779
2^85201+1 = 42242438046141300343249
2^85213+1 = 66923847934539231299
2^85229+1 = 108856251563201
2^85229+1 = 174625707352253815363
2^85247+1 = 825460142721102879961
2^85297+1 = 20890748999767496403161
2^85331+1 = 429734853667011523504561
2^85361+1 = 195763592020375019
2^85427+1 = 19905456895318219987
2^85427+1 = 30722356603479641104531
2^85439+1 = 392698207240992307
2^85439+1 = 6610370830425559206931
2^85447+1 = 282558238734025418971
2^85453+1 = 1576833041364538088161
2^85487+1 = 3327038769329201
2^85487+1 = 671600762587055223673
2^85513+1 = 481985684575043617649
2^85513+1 = 5097466089814763655689
2^85571+1 = 25745914785038532807773233
2^85577+1 = 1756773244780354970171729
2^85577+1 = 279533982460507
2^85601+1 = 5468264266944833
2^85639+1 = 2994269199306787
2^85643+1 = 7283178874441304617
2^85667+1 = 103402664896368941514504113
2^85717+1 = 478420503455913808129
2^85717+1 = 91677596269747565318971
2^85751+1 = 194375405476735150979249
2^85817+1 = 11508524064883603
2^85819+1 = 1737075568802367220283
2^85829+1 = 38411535680823611
2^85829+1 = 65824939018780121
2^85837+1 = 1712534535881471947259
2^85847+1 = 7105680519855145097
2^85847+1 = 9430031189448257
2^85853+1 = 465547594387119107
2^85853+1 = 7026484061267383103655203
2^85903+1 = 18429305919270949405337
2^85909+1 = 11216852013031456873
2^85931+1 = 135219522000818683633
2^85999+1 = 18316172626730548483
2^85999+1 = 200154639712705766162461889[/CODE]

 axn 2019-01-30 15:54

86k-90k
[CODE]2^86017+1 = 29374286987144597747
2^86029+1 = 3734488040860891
2^86069+1 = 3262027500821521
2^86069+1 = 955885424361523
2^86077+1 = 15802504134579913
2^86111+1 = 22783955077707625259
2^86113+1 = 2019406890045619
2^86113+1 = 27014425378671833
2^86113+1 = 3542687801310077257
2^86143+1 = 77890681773742230538786937
2^86161+1 = 104420172529264897
2^86249+1 = 17347309692547933365478163
2^86249+1 = 18898639420922059
2^86263+1 = 318980743023229826327048131
2^86269+1 = 1641666359555809
2^86291+1 = 3148814203514009
2^86293+1 = 170186414625741859
2^86297+1 = 21172467495262609313
2^86297+1 = 827384730118486513
2^86311+1 = 226740241414865131164353
2^86311+1 = 270439812733606354961
2^86351+1 = 3779491176411090036054331
2^86353+1 = 176181131125268041
2^86353+1 = 17694500403662204491
2^86369+1 = 440598072099762365574091
2^86371+1 = 32169172406460791363
2^86389+1 = 1699678570567841
2^86399+1 = 2013901409226929
2^86413+1 = 1749118584417067
2^86467+1 = 79890162015576293153153
2^86477+1 = 6257023603888819
2^86531+1 = 261527462807321
2^86531+1 = 708376232759578609563283
2^86533+1 = 1654357940788433363809
2^86533+1 = 207334181520094862587
2^86539+1 = 20890916876714579
2^86573+1 = 2875609502139041
2^86573+1 = 3727432975026913
2^86599+1 = 83147932463535769
2^86677+1 = 3831794759838607091
2^86753+1 = 1034905364540927032934281
2^86753+1 = 297898540609206059
2^86767+1 = 154005193468942780840321
2^86771+1 = 17916526956093347
2^86771+1 = 22037009365624031401123843009
2^86771+1 = 315789663857501565803
2^86783+1 = 2647096388546190848373907
2^86783+1 = 45826931873848257902177
2^86837+1 = 489864899728981403440067
2^86843+1 = 164159701707776513
2^86843+1 = 89994235990314276497
2^86869+1 = 34527918206617084927499291
2^86869+1 = 366860787096706736162224019
2^86951+1 = 134596433974987
2^86969+1 = 2787923011857091819
2^87103+1 = 14561529994701279460723
2^87107+1 = 54961708272492080074027
2^87119+1 = 1520597773033476667
2^87133+1 = 23329490677069208338667
2^87151+1 = 750223729931317704809
2^87151+1 = 79845510616470372251
2^87179+1 = 476379745278403
2^87221+1 = 212039884778833
2^87257+1 = 13074609079646473
2^87257+1 = 8339147477791381931
2^87257+1 = 83861178088455409
2^87277+1 = 10907163811204652231921
2^87299+1 = 184257545949518311547
2^87299+1 = 395913534136482397731467
2^87317+1 = 3461964896809611793561
2^87323+1 = 164267218517521858993
2^87323+1 = 92264618734835037523
2^87383+1 = 16482960806781853618417
2^87403+1 = 32358460362713752077721
2^87407+1 = 133605916419580693257515881147
2^87407+1 = 45598949847787601388370531
2^87407+1 = 7251001054916249
2^87421+1 = 11438514310740584147
2^87421+1 = 21876925934803230480769
2^87473+1 = 3691044960284675069457020257
2^87511+1 = 313635967521870365443
2^87517+1 = 53106625835743498426873
2^87541+1 = 974421499125262651
2^87559+1 = 115771262616785282827
2^87589+1 = 14982349652592097249
2^87589+1 = 873419896236622937
2^87613+1 = 2373145066898319243883
2^87613+1 = 2911990063050908537
2^87641+1 = 275800902809251
2^87641+1 = 3660315898495799530627
2^87671+1 = 1438999327499939
2^87671+1 = 369353784928801
2^87683+1 = 497005086231109867687739
2^87697+1 = 91439719005523007038324529
2^87719+1 = 1150232398670233
2^87719+1 = 148222010253979
2^87739+1 = 803781108054194873
2^87797+1 = 34426785297634033
2^87803+1 = 39792673706951119024339
2^87853+1 = 4765627135345201
2^87881+1 = 73236823191016984307
2^87943+1 = 2715416883936816539
2^87959+1 = 244603867198176401
2^87961+1 = 13033634810528446369
2^88007+1 = 1532663334176459
2^88007+1 = 6111181272410827
2^88069+1 = 104739216756617
2^88069+1 = 785950603893743081177
2^88177+1 = 298692579938546483
2^88177+1 = 92299416903588391499356258043
2^88211+1 = 581613150856662193
2^88223+1 = 48158407515897643
2^88241+1 = 180055438029265889
2^88261+1 = 11651374789597077694099
2^88321+1 = 263104089542233
2^88339+1 = 29503160062315010009
2^88339+1 = 6440964877400028145071649411
2^88339+1 = 914277633445073399483
2^88379+1 = 34474961176007558633186217885979
2^88469+1 = 2324335311257129363
2^88471+1 = 13470017617728382069507
2^88471+1 = 18368075442719179
2^88493+1 = 4641968235317587434910057
2^88513+1 = 159437117840809263211
2^88591+1 = 18535151200647012977
2^88591+1 = 433468067631377
2^88721+1 = 2707393584042465160547
2^88747+1 = 336829527573760259
2^88771+1 = 11767915386614235236753
2^88799+1 = 24696442107187130353
2^88801+1 = 220459908592757865714611
2^88807+1 = 945342246535459
2^88811+1 = 315596233918215625409
2^88811+1 = 676211905522695436740277409
2^88817+1 = 470006968948111801913801
2^88819+1 = 177030698144850833
2^88843+1 = 43183278629727731616420272747
2^88993+1 = 84785096478842052659
2^89041+1 = 138237318799620697
2^89069+1 = 251583528513775155571
2^89069+1 = 6422609571534686061855929
2^89101+1 = 135603855046486114304870590897
2^89113+1 = 222768300120493049249
2^89123+1 = 133338916490322451
2^89209+1 = 1194731181725216297
2^89213+1 = 5860280610604220257
2^89227+1 = 1975797317855041
2^89231+1 = 7439172507338294807131
2^89237+1 = 18021187980904139929
2^89269+1 = 802173493166469139
2^89303+1 = 243882855688811
2^89303+1 = 5508395854255919145043
2^89363+1 = 54725307764191755259
2^89381+1 = 6436140830732281585835063257363
2^89387+1 = 1724092932722009
2^89393+1 = 163068013255619
2^89393+1 = 33995735711562078612814211
2^89393+1 = 4264170625879289
2^89393+1 = 90876275027799497
2^89399+1 = 4060980819625179720971
2^89413+1 = 1636021043498951539
2^89477+1 = 127702161075278247817
2^89519+1 = 104928056028516112267
2^89533+1 = 15848169733495357723
2^89591+1 = 232993805054448261186899
2^89591+1 = 39127558456846791696091
2^89591+1 = 819593410026220859
2^89627+1 = 292422408355453668066286651
2^89653+1 = 72618059740486443501529
2^89669+1 = 19899416537579602843
2^89681+1 = 143398402919019217
2^89689+1 = 9118162327314169
2^89753+1 = 208366505974584606289
2^89767+1 = 87561338237291728819
2^89783+1 = 395344870952901041
2^89783+1 = 8244274764210637267
2^89809+1 = 76548673198784445961
2^89821+1 = 22173041308123297
2^89839+1 = 1845766811225968249523
2^89849+1 = 72356421401910379
2^89867+1 = 11570846816213696036910491
2^89891+1 = 190929809173123
2^89897+1 = 338599099797989970707
2^89923+1 = 6612026472628626347
2^89963+1 = 147265370250107
2^89983+1 = 11350583880777243676003[/CODE]

 axn 2019-02-03 02:09

90k-93k
[CODE]2^90011+1 = 106170375963956393
2^90017+1 = 1156134455712420307
2^90053+1 = 18169760780503595550401
2^90053+1 = 47550211091818592501939377
2^90071+1 = 3487278705924625165512121
2^90121+1 = 41411569766017425691
2^90121+1 = 6143861397294233
2^90149+1 = 509038367391180528859
2^90173+1 = 5194898154031793
2^90187+1 = 22617540501326178857
2^90197+1 = 223281251294279739641
2^90203+1 = 12945831167924570320016419
2^90227+1 = 19791871633154588076427
2^90227+1 = 19913469529959251
2^90239+1 = 535980163623267131
2^90247+1 = 21092932913178795735506849
2^90271+1 = 317812210895578667
2^90289+1 = 504960911114355071622739
2^90359+1 = 30413192830287938171
2^90397+1 = 508413811182346207763
2^90401+1 = 43945831497064369
2^90403+1 = 315219782570073923351301091
2^90499+1 = 1824224320869486089
2^90583+1 = 4965575942987027
2^90599+1 = 805072203039686071393
2^90631+1 = 1105076504130839587
2^90631+1 = 647548238146714283
2^90641+1 = 1234424766131171
2^90679+1 = 236860800798763836619
2^90709+1 = 10271789426495041
2^90833+1 = 106884802867971380113
2^90841+1 = 140599718832161731
2^90911+1 = 4351351285367179
2^90971+1 = 2209944692995852519829497
2^90971+1 = 244396217930108971
2^91081+1 = 27485827789080643
2^91099+1 = 105793047004176570552707
2^91129+1 = 388058857441218011
2^91139+1 = 5711122763368458731
2^91141+1 = 108491184056749259
2^91141+1 = 36367954512027227
2^91163+1 = 5222343808994205819466209148140953993
2^91237+1 = 746629280018684264681
2^91243+1 = 149156802290982289
2^91249+1 = 58000232143851857809
2^91291+1 = 14464147810111310489
2^91331+1 = 1112555185211161
2^91331+1 = 57334991341556249
2^91367+1 = 124281680925190557396269809
2^91381+1 = 1486862351146230086655019
2^91387+1 = 3750938635116885504137
2^91387+1 = 70748986179954940620986683
2^91397+1 = 812344219197409
2^91411+1 = 7575536561429703379
2^91453+1 = 39872457883977073
2^91459+1 = 4592833035345113973507913
2^91529+1 = 29548513015818075187
2^91573+1 = 881608198162089353209
2^91577+1 = 28101522986172001
2^91591+1 = 1293743743409906196995513
2^91703+1 = 1407573587045905831726197811
2^91711+1 = 1083376863162721
2^91711+1 = 184929394174972398041
2^91711+1 = 660458388500747
2^91753+1 = 19846177333619682667939
2^91753+1 = 358133082018190313
2^91801+1 = 2045086205469472020498069593
2^91807+1 = 1543893404699656403
2^91807+1 = 1994835827053529
2^91807+1 = 64787069135108717095057
2^91811+1 = 15492833898364752540034169
2^91813+1 = 3550735370456007935811097
2^91837+1 = 8270955931873276315624635467
2^91909+1 = 61050824568238685707
2^91921+1 = 1232491760056434307
2^91957+1 = 4109503195458350012459
2^91961+1 = 3520420242159104304409
2^91967+1 = 171283768780187441957849
2^92003+1 = 79127761152506264452403
2^92009+1 = 78829546743958019
2^92033+1 = 23834968834943793008721137
2^92041+1 = 42949354717325272297
2^92083+1 = 662565038818339
2^92111+1 = 11639609531354656309162673
2^92119+1 = 4720649029951657315339
2^92143+1 = 408087000520848613549121
2^92143+1 = 875308405720907
2^92173+1 = 32424500401013348311811
2^92173+1 = 7275350135903027617
2^92189+1 = 136924443868017236969
2^92219+1 = 1277959251714041297
2^92219+1 = 642942640109312181072457
2^92227+1 = 786760451417274562378123
2^92233+1 = 958153370107984593552169
2^92237+1 = 17807914577050311299
2^92243+1 = 299922013227527819
2^92243+1 = 40137981108817098252803
2^92297+1 = 34061092334613451
2^92311+1 = 1241879599192801255019
2^92357+1 = 2393424090851536792795657
2^92377+1 = 233832249877273
2^92377+1 = 2371896257557950715841
2^92383+1 = 8177486948725985713
2^92399+1 = 324503043813089
2^92401+1 = 4657846728988983342107411
2^92419+1 = 5571292151740603
2^92459+1 = 10543393965288421836584005931
2^92461+1 = 112338842744050905963857
2^92567+1 = 38044969540635979626737
2^92581+1 = 1211109737101194793867
2^92593+1 = 679630129909135500257
2^92623+1 = 25635457215193815617
2^92627+1 = 428742764475958981859
2^92627+1 = 44124264037752641921
2^92639+1 = 735839440767494017
2^92647+1 = 26625224383699603
2^92693+1 = 3583400010012309760561
2^92699+1 = 1180866742093926086497
2^92699+1 = 1428377370554384405621803
2^92699+1 = 40024718330084796521
2^92737+1 = 1657819612439473938646643
2^92767+1 = 18387148795894628321369467
2^92767+1 = 21925093377554170184753
2^92767+1 = 300330253883483
2^92789+1 = 25836084868773837227729
2^92809+1 = 1459174603314377
2^92831+1 = 2070500493032509408121
2^92831+1 = 937529280358459
2^92857+1 = 82391570276539026161
2^92863+1 = 416631542419852640129
2^92893+1 = 1263328606548164329
2^92951+1 = 918743959591455817
2^92951+1 = 931119765268510427
2^92993+1 = 1658399398658617[/CODE]

 axn 2019-02-06 03:24

pay dirt!

[CODE]ECM found a factor in curve #160, stage #1
Sigma=54626733384473, B1=1000000, B2=100000000.
2^9181+1 has a factor: 76784137749059091145875053513 (ECM curve 160, B1=1000000, B2=100000000)
Cofactor is a probable prime![/CODE]

So, (2^9181+1)/3 = 3011369 · 76784137749059091145875053513 · 830850377585029456002515680049587 · PRP2695

Note that the p33 was already known, but the p29 was missed. And the p29 was found in stage 1 !!

Someone want to take a crack at a juicy PRP2695?

 paulunderwood 2019-02-06 03:58

Congrats again :toot:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^9181+1)/3/3011369/76784137749059091145875053513/830850377585029456002515680049587" | ../../coding/gwnum//bpsw-2 - 1 2 9181 1

Testing (2*x)^((n + 1)/2) == -2 (mod n, x^2 - 9*x + 1)...
Likely prime!

real 0m0.600s
user 0m0.328s
sys 0m0.024s
[/CODE]

 paulunderwood 2019-02-06 04:41

[QUOTE=axn;507784][CODE]ECM found a factor in curve #160, stage #1
Sigma=54626733384473, B1=1000000, B2=100000000.
2^9181+1 has a factor: 76784137749059091145875053513 (ECM curve 160, B1=1000000, B2=100000000)
Cofactor is a probable prime![/CODE]

So, (2^9181+1)/3 = 3011369 · 76784137749059091145875053513 · 830850377585029456002515680049587 · PRP2695

Note that the p33 was already known, but the p29 was missed. And the p29 was found in stage 1 !!

Someone want to take a crack at a juicy PRP2695?[/QUOTE]

That should not take Primo a long time to prove.

 axn 2019-02-06 13:27

93k-96k
[CODE]2^93001+1 = 13744425055923816992411
2^93059+1 = 812334798111654241
2^93077+1 = 63299563986510730633
2^93083+1 = 68259027888543693457
2^93103+1 = 34207268600198531
2^93103+1 = 37071449024261357842249
2^93169+1 = 5727062687274848779
2^93179+1 = 20078412822489768841
2^93229+1 = 939584799186068466947
2^93241+1 = 3778521656575496325128443
2^93251+1 = 930577510290473
2^93283+1 = 740870310129969137
2^93287+1 = 5764428381514513
2^93287+1 = 7718689223866507
2^93307+1 = 15285653767400751934097
2^93307+1 = 9321950497097470297873523
2^93323+1 = 143496334074667267
2^93323+1 = 2208565311452188807883
2^93383+1 = 162580840485131
2^93407+1 = 1546390279590512009
2^93479+1 = 513851049050083
2^93497+1 = 2583904067662441499
2^93503+1 = 344775577707073
2^93503+1 = 8664649853494518347
2^93523+1 = 13847764441619833
2^93563+1 = 103295270378059
2^93581+1 = 697903278768926809
2^93701+1 = 239765148153331
2^93701+1 = 7517720098185022217
2^93719+1 = 399089727103655633
2^93761+1 = 651243774388169
2^93761+1 = 9830883632650343666930411243
2^93763+1 = 524346886103897
2^93811+1 = 3199129231931715083726115593
2^93893+1 = 7143473692046833
2^93901+1 = 13019341692860473
2^93901+1 = 623317986153275275307
2^93937+1 = 3999457171091361327377
2^93979+1 = 2117005202117483198539
2^93997+1 = 143538967266923
2^93997+1 = 37108584799857279489073
2^94007+1 = 11949964406685420794963
2^94009+1 = 166243987228940611
2^94049+1 = 147520930173737902547
2^94049+1 = 1514914601287301017
2^94049+1 = 5650364380795577
2^94117+1 = 2243895624665402921
2^94121+1 = 248992472375703769
2^94153+1 = 261476009935867845011683
2^94169+1 = 887910193812993097407337
2^94219+1 = 15179209059689799826312411
2^94219+1 = 28782004487799189156113
2^94219+1 = 7269028858966928563
2^94219+1 = 75651401056749949143481
2^94291+1 = 14975308419198577
2^94291+1 = 39624005418646739
2^94327+1 = 262563619758217
2^94327+1 = 41335816463415570472531
2^94351+1 = 1347675889558089313
2^94379+1 = 297986408742294123113147
2^94397+1 = 167208522114896626153
2^94399+1 = 2755437910877074523
2^94433+1 = 19451309034942216527681
2^94439+1 = 40325948381469680051
2^94447+1 = 3490043240442217
2^94483+1 = 436836185755839179371
2^94543+1 = 653553905209889107
2^94547+1 = 421574522878459
2^94547+1 = 825879298992830824556838787
2^94559+1 = 38075714101039232001193
2^94561+1 = 2450234300530533930419
2^94597+1 = 40383937842417123855161
2^94603+1 = 272610652737971
2^94621+1 = 310400785659639179
2^94649+1 = 1597990066629779
2^94687+1 = 663056134955097538763
2^94709+1 = 701891799284859736692206051
2^94727+1 = 2497919529511829483
2^94771+1 = 48874108171142525897
2^94771+1 = 787227040800658820617
2^94777+1 = 11602183099371209083
2^94789+1 = 21038773316323938121
2^94793+1 = 1879568282825730551617
2^94811+1 = 2148329961202874458601
2^94823+1 = 591804735425585270376211
2^94933+1 = 22940108546427063731
2^94933+1 = 369594467953793
2^94949+1 = 1369840871938840129
2^94961+1 = 152074402717024975512683
2^94961+1 = 98703644485855792651
2^94999+1 = 12436250356844428987779779
2^95063+1 = 155748361152563203291
2^95063+1 = 1564962497411674084187
2^95107+1 = 107715190508581379
2^95111+1 = 104048433818617
2^95143+1 = 198701843233339993
2^95153+1 = 1260883994234698320451
2^95153+1 = 69720179311951900939
2^95177+1 = 1138543230950999827
2^95239+1 = 307811488616758707697
2^95257+1 = 1738711857617699
2^95257+1 = 3555040961482880173657
2^95279+1 = 17594484882340685873
2^95287+1 = 19980712161844006732307
2^95327+1 = 12790940787309931
2^95327+1 = 3791160361770572230681
2^95339+1 = 342564658515118673
2^95383+1 = 848606186094905959979
2^95401+1 = 1741112842144619
2^95401+1 = 30612399784386075176467939
2^95443+1 = 1355682230259985415295611
2^95467+1 = 12161752843008694019
2^95467+1 = 256013403506887046949937
2^95467+1 = 724794291236158327153
2^95471+1 = 49562804389443080227
2^95483+1 = 787120775213401
2^95507+1 = 1004943086851001
2^95507+1 = 3416046669680459
2^95527+1 = 1242714171842737811963
2^95569+1 = 74325704889242493209
2^95581+1 = 65884124564130113
2^95581+1 = 9592936004391958187491
2^95603+1 = 776479891078135290247667
2^95633+1 = 32055938578310360699
2^95651+1 = 1088744548112142119908921
2^95651+1 = 48573029969233013830784083
2^95707+1 = 38143394293510890550619
2^95731+1 = 2458185244296307
2^95737+1 = 15096455641830881
2^95737+1 = 214849044042811769
2^95737+1 = 660419822807929
2^95783+1 = 10751699252886713825603
2^95819+1 = 390809021486801
2^95869+1 = 132886331574353823385939
2^95869+1 = 854145482660425913
2^95971+1 = 4969917621352679729[/CODE]

 DukeBG 2019-02-06 20:32

Ok, since noone still uploaded a cert for that PRP2695, i'll do it then.

 axn 2019-02-11 17:00

96k-100k
[CODE]2^96001+1 = 29767258628107316819
2^96013+1 = 1074062209085419541841673
2^96059+1 = 162271396235077769
2^96059+1 = 20512561145349960215675737
2^96079+1 = 39853885691623733272441
2^96149+1 = 1267670031135796879290547
2^96181+1 = 1562575760853467
2^96181+1 = 4007722130435761
2^96221+1 = 44037051941095219
2^96233+1 = 1185623668212455203
2^96263+1 = 160566383673660547939
2^96263+1 = 3158222404244412047329
2^96269+1 = 1548599154891831184721
2^96269+1 = 1860502872298768793
2^96337+1 = 435649543301037672707
2^96353+1 = 314407631381596999426811227
2^96401+1 = 2802994608065303519689
2^96401+1 = 5711563827628019
2^96443+1 = 292171176753089
2^96443+1 = 5615664589725452306953
2^96451+1 = 3368804501343929513
2^96461+1 = 155013189693361
2^96461+1 = 231703520947331
2^96469+1 = 320787082864072929109211
2^96479+1 = 14286832806147281360579
2^96493+1 = 3144148189426106687137
2^96527+1 = 214317110285594417
2^96553+1 = 142572499472297
2^96589+1 = 178693936137068179
2^96589+1 = 457065989038013497
2^96661+1 = 334575205692201996331
2^96731+1 = 4093111383382080931
2^96739+1 = 14272248893509138536689
2^96757+1 = 10906820693119187
2^96757+1 = 6475518092372133264569
2^96763+1 = 484745206418193961
2^96763+1 = 68704402071619676498528059
2^96847+1 = 16278825648714713496179
2^96893+1 = 21860035804117719347
2^97001+1 = 6323433518478887453009
2^97007+1 = 2919520998904749881
2^97073+1 = 13108033656310688129
2^97073+1 = 28188797235272619766259
2^97073+1 = 9863128724570411009
2^97081+1 = 37997114714506275971
2^97103+1 = 646582148549901711361
2^97169+1 = 192580760045809
2^97177+1 = 726564097045651
2^97241+1 = 212246581189403
2^97241+1 = 6973894407688699889
2^97259+1 = 1557828531578176056833
2^97283+1 = 213350641219987
2^97303+1 = 17360942024884000019
2^97367+1 = 394359267905704628281
2^97387+1 = 1184686534292445731
2^97429+1 = 60175019356103987
2^97441+1 = 1670478734921369810188185521
2^97459+1 = 565306383931518998497
2^97459+1 = 67427656986769546969
2^97499+1 = 1026481948021709054213579
2^97499+1 = 347130741513187
2^97499+1 = 36284001069947387
2^97501+1 = 328557552611617072938553
2^97501+1 = 43283615473583504939
2^97501+1 = 7902421905950283211
2^97547+1 = 5494965405945903024091
2^97549+1 = 3207878769085809763883
2^97553+1 = 22356781474632417519812251
2^97571+1 = 23608466666870205161
2^97571+1 = 770583394973772403
2^97577+1 = 46931258519544749459
2^97583+1 = 224554429504671907
2^97583+1 = 2955030691318006678043
2^97609+1 = 25687897097511983641243
2^97613+1 = 181964747330961479587
2^97613+1 = 338773060886835769
2^97649+1 = 2021994048123593310579083
2^97777+1 = 280868367534778339
2^97787+1 = 483780424355370043729
2^97813+1 = 936727200377960867
2^97843+1 = 2234972710366886629038569
2^97919+1 = 492417738210785603
2^97943+1 = 426494208265479313
2^98011+1 = 39106146691855183489
2^98017+1 = 302038062458172328321507
2^98047+1 = 67049977459938481149793
2^98123+1 = 1878817043441920993
2^98123+1 = 3667334414342827
2^98129+1 = 2484647951593393
2^98129+1 = 50060806747597721
2^98179+1 = 454899938128553841947
2^98207+1 = 14227482997804963
2^98227+1 = 60938591664197241322955489
2^98251+1 = 1113136956482270075347
2^98251+1 = 641202077069369
2^98297+1 = 14501842174986825374003
2^98299+1 = 110868633842069531
2^98321+1 = 160239344512375953890050217
2^98327+1 = 1254709843262062153
2^98347+1 = 298337992547059337
2^98387+1 = 46347629908531249255187
2^98389+1 = 400187257242041
2^98407+1 = 517038810573070638371
2^98407+1 = 82785375216088825801
2^98407+1 = 987418132994436355609
2^98411+1 = 39185070939485121113
2^98429+1 = 2466250991913053767243139
2^98453+1 = 2266725956110324283
2^98467+1 = 1138778298908267
2^98479+1 = 15150366101928966938179
2^98491+1 = 478546518345264619
2^98561+1 = 131909422022394644532379
2^98563+1 = 509536599316961
2^98621+1 = 47029159981184713
2^98627+1 = 1850676398834609179
2^98639+1 = 105531571954139
2^98639+1 = 4612949520652126956933971
2^98689+1 = 171309063220465996729
2^98711+1 = 55377473890208664731
2^98717+1 = 64479879981329803
2^98729+1 = 154621438680906947
2^98729+1 = 6817329680592233610331
2^98779+1 = 99990810853902221601043
2^98809+1 = 7281671108520441346033
2^98873+1 = 1704796827253871587
2^98873+1 = 37084837271396231125507
2^98893+1 = 1706296511260147
2^98893+1 = 71477325864973849
2^98899+1 = 35575692015878171
2^98911+1 = 329434637599762393
2^98911+1 = 627533926598142859
2^98929+1 = 1845544993023440853073
2^98939+1 = 12085096429740050092522577
2^98939+1 = 221098704494393592458659
2^98939+1 = 31542297979461977239008523
2^98953+1 = 11215665208046306057
2^98953+1 = 571657825074737
2^98981+1 = 16811033392044817320158348325259
2^98981+1 = 32438991475815066222313
2^98981+1 = 73277570035096032353634553
2^98993+1 = 91444367272985953
2^98993+1 = 98098060359565102156553
2^98999+1 = 1051299667269040394483
2^98999+1 = 38461666007346763838345473
2^99013+1 = 17279923859372716057
2^99041+1 = 11264740878746521
2^99041+1 = 28843535851083319422403
2^99053+1 = 38926586794750859
2^99079+1 = 11062205977817611
2^99079+1 = 1936502015480521
2^99089+1 = 834465867780470973001
2^99089+1 = 9008408934029613169
2^99133+1 = 1590360090075257
2^99133+1 = 3886669924917862729
2^99137+1 = 4852645561922463979
2^99149+1 = 2806267196992899569
2^99149+1 = 611664983327010241
2^99173+1 = 34117345390446566429876483
2^99181+1 = 1429330789505633472713
2^99191+1 = 2586809772952026403
2^99241+1 = 141936170324449378568443
2^99241+1 = 594534674660569
2^99277+1 = 137735140213676980057
2^99277+1 = 47819621653128877322977
2^99317+1 = 11120228658226147
2^99349+1 = 12181448518519827635339
2^99367+1 = 7682051224167095803193
2^99391+1 = 1799299151631295913
2^99397+1 = 53375555142562615629371
2^99409+1 = 141334122256753
2^99431+1 = 12172936497590971640963
2^99469+1 = 1039733312799687579377
2^99469+1 = 16942130366484989507987
2^99469+1 = 40450480970809649
2^99469+1 = 632609919374777
2^99487+1 = 13874905407710027
2^99523+1 = 34399598608921528523
2^99527+1 = 35435947200240513193
2^99551+1 = 118646658835324603
2^99551+1 = 956620131867689
2^99563+1 = 97559166174873817291
2^99571+1 = 2794271080961462753767169
2^99607+1 = 130373578560167962112307817
2^99623+1 = 3906368490735110522777
2^99643+1 = 17912196731662598513563
2^99643+1 = 448204908352752089827
2^99667+1 = 34872671165705318168507
2^99679+1 = 509833420640384323725001
2^99713+1 = 1408106736245825121017
2^99721+1 = 803326104268803977
2^99793+1 = 345231747036597680656560489989737
2^99793+1 = 57024817298211817963
2^99809+1 = 4144518991661456011
2^99859+1 = 676669031242767095260921
2^99871+1 = 186316649204205313193
2^99871+1 = 26692861657976342060873
2^99871+1 = 3588603004538820773969
2^99881+1 = 53186256007200218401
2^99881+1 = 566631967992209316697393
2^99929+1 = 2530207524851137580146374617
2^99961+1 = 1623728942646841
2^99961+1 = 2902878543528934211[/CODE]

 axn 2019-02-16 18:17

9-9.5k to t35
[CODE]2^9391+1 has a factor: 15053695523301896080196014623082123 (ECM curve 556, B1=1000000, B2=100000000)
2^9397+1 has a factor: 142431182933424549568492130623460569 (ECM curve 863, B1=1000000, B2=100000000)
2^9277+1 has a factor: 43121574137546761051397200211457141787 (ECM curve 558, B1=1000000, B2=100000000)
2^9181+1 has a factor: 76784137749059091145875053513 (ECM curve 160, B1=1000000, B2=100000000)
2^9137+1 has a factor: 3327060733378993953616723390060019 (ECM curve 218, B1=1000000, B2=100000000)
[/CODE]

 GP2 2019-02-16 23:36

With ECM to t40 on Wagstaff exponents from 3000 to 4000, the following factors were discovered:

[CODE]
2^3011+1=1816619272155487791560717448516519693937
2^3089+1=13839103247628681510101111834057993
2^3109+1=590010984386508367122063204267363841,73386299644848640204126072658168681,83316512557326177817598047246790849469030361
2^3167+1=33152238124362923032373534255518409
2^3319+1=3252360285900453519800855046203605362811
2^3373+1=2542916407539550917982537085402937903019
2^3433+1=166596781182097605569132789924365551329
2^3449+1=1237042874546529851324382493065770076641153
2^3533+1=22073945862359767285266685333132481441427377
2^3571+1=1222019590737291558255575120183884699,276256789208754723404276460523
2^3581+1=148503017368476924146456255256881776747
2^3637+1=4079937169947205097853033549950017
2^3739+1=13394841132851831667530611640122193957306923
2^3793+1=84623495188538318097610966381339248486660083
2^3823+1=3221770714648236848248157965151857
2^3943+1=361015976299864394671296312524737187
2^3947+1=7499425548876402914429380134327605947
[/CODE]

Unfortunately, none of them resulted in PRP cofactors. Maybe the 4k range will have some.

 axn 2019-02-26 10:03

100k-102k (t25)

[CODE]2^100129+1 = 25688950465586276971
2^100153+1 = 10720388598267921491
2^100153+1 = 5804229203262904241929
2^100169+1 = 5224437302402897057
2^100183+1 = 1788066096394188801297139
2^100213+1 = 56427141679506021889
2^100313+1 = 295567952996905219
2^100361+1 = 346316081878860965891
2^100417+1 = 1079676713189299073
2^100447+1 = 8547924742232949613889
2^100483+1 = 2698219793672669380817
2^100517+1 = 547364738235344753
2^100523+1 = 28611607422832825133073563
2^100523+1 = 503050835622099817487651
2^100547+1 = 10416634164049354099
2^100613+1 = 23139905183450018500441
2^100649+1 = 294840528094662732841
2^100673+1 = 6836026999276557292565963
2^100741+1 = 511058179677748106800931
2^100747+1 = 16014062648121269297
2^100747+1 = 311493111436876123
2^100769+1 = 251704259406499772489
2^100799+1 = 15600106075574524619
2^100847+1 = 10897918234335228638929
2^100913+1 = 113047892664847606451
2^100931+1 = 41855348903947886537
2^100937+1 = 164914506066167955151163
2^101009+1 = 908005007023408875265297
2^101009+1 = 93918088342486619
2^101021+1 = 21562997855965633201
2^101027+1 = 628229657566606649
2^101081+1 = 357475580384275799911963
2^101089+1 = 3619771874989322264378243849
2^101107+1 = 7613068550525042390829227
2^101111+1 = 2584883841472434449659979
2^101113+1 = 330267544782864993851467
2^101159+1 = 6183893989348928753
2^101173+1 = 3277923133271759729
2^101173+1 = 355523335501340051284009
2^101197+1 = 90597010926048481
2^101203+1 = 473122075605766319233
2^101273+1 = 12642834809888473417
2^101279+1 = 5022803416251338281
2^101287+1 = 13540811660726487718969
2^101323+1 = 3100799453710889645579
2^101359+1 = 28938775713646528309193
2^101399+1 = 1534971040557222903499
2^101411+1 = 161002222537092210419
2^101429+1 = 16005524784003474113
2^101429+1 = 181163111425417912817177
2^101429+1 = 5062240980850911964753
2^101477+1 = 587811113797798660102771
2^101489+1 = 1800762843842270840963
2^101489+1 = 40798751767261835647169
2^101513+1 = 2405834159029917937259
2^101527+1 = 12076299431481925159078043
2^101537+1 = 6925989208339669730257
2^101561+1 = 3855946849405070079889
2^101611+1 = 385472013663595196017
2^101611+1 = 647534575861668288991051
2^101611+1 = 769829805249776603
2^101681+1 = 241823992867052143169
2^101693+1 = 4700534847636745529
2^101723+1 = 137144872755949430419
2^101737+1 = 143993392494482339
2^101737+1 = 268867336515506694425479147
2^101737+1 = 556160539329438675713
2^101749+1 = 595442369433608483
2^101749+1 = 980704466315833219
2^101837+1 = 11030690951278414627
2^101869+1 = 6486800532155769521273
2^101921+1 = 3267585635210320049020097
2^101921+1 = 77398645622382749756761
2^101957+1 = 78485507759851289
2^101987+1 = 1688174075177787927803
2^101999+1 = 329009834647766099[/CODE]

 axn 2019-03-02 02:53

[CODE]ECM found a factor in curve #79, stage #2
Sigma=8182130021064353, B1=50000, B2=5000000.
2^102299+1 has a factor: 338189324089623539623841 (ECM curve 79, B1=50000, B2=5000000)
[/CODE]
I guess at this size P95 doesn't do PRP testing of the cofactor, because factordb tells me...
[c](2^102299+1)/3 = 28439123 · 338189324089623539623841 · PRP30764[/c]

[CODE]No factoring at all, not even trivial division
Primality testing (2^102299+1)/28853423355215000601173363794329 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000001257801520.txt
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX FFT length 10K, Pass1=128, Pass2=80 on A 102195-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX FFT length 10K, Pass1=128, Pass2=80 on A 102195-bit number
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.19% proof)
(2^102299+1)/28853423355215000601173363794329 is Fermat and Lucas PRP! (117.4538s+0.0049s)[/CODE]

 GP2 2019-03-02 16:33

[QUOTE=axn;509842][CODE]ECM found a factor in curve #79, stage #2
Sigma=8182130021064353, B1=50000, B2=5000000.
2^102299+1 has a factor: 338189324089623539623841 (ECM curve 79, B1=50000, B2=5000000)
[/CODE]
I guess at this size P95 doesn't do PRP testing of the cofactor, because factordb tells me...
[c](2^102299+1)/3 = 28439123 · 338189324089623539623841 · PRP30764[/c]
[/QUOTE]

Yes, at some point the PRP test is no longer quick and Prime95/mprime no longer does it.

Since we have 2048-bit PRP residues for all Wagstaff exponents under 2M, I automatically run Gerbicz cofactor-compositeness tests whenever new factors are discovered in this exponent range. This test is much faster than a PRP test, although it can only find probable probable primes as opposed to actual probable primes.

 axn 2019-03-10 02:00

102k-104k (t25)

[CODE]2^102001+1 = 770957355196573817
2^102079+1 = 24715796754544855891
2^102101+1 = 12170646087469408474433
2^102103+1 = 2851129637373075299332307
2^102107+1 = 87729566611955022309827
2^102149+1 = 17030667459639752873
2^102199+1 = 2371496814296641421393
2^102233+1 = 653638095872549987
2^102253+1 = 601892013365499238937
2^102299+1 = 338189324089623539623841
2^102329+1 = 6366383123951716845872953
2^102407+1 = 792658079943930763
2^102437+1 = 28737481410188638753
2^102481+1 = 2568630649986400787
2^102497+1 = 156684370103469559042723
2^102593+1 = 2835946408661279641702033963
2^102593+1 = 644356899066626499176483377
2^102653+1 = 434623901028640506804688609
2^102667+1 = 4439541201846151702289
2^102673+1 = 278110463166412691
2^102701+1 = 539666767691108505137
2^102763+1 = 1131690627764983729
2^102811+1 = 1613814476488071564011
2^102811+1 = 318299121313111129
2^102859+1 = 484380393296447905171
2^102871+1 = 12506148369290004281467
2^102911+1 = 23662826326380733621578601
2^102911+1 = 305263125371843323
2^102967+1 = 149200424330765900075777
2^103043+1 = 51277801637576309569
2^103091+1 = 152869215642589561
2^103141+1 = 394938112991962822222403
2^103349+1 = 4081333819139643086561
2^103357+1 = 4756568416003264507
2^103391+1 = 68101445363099340166627
2^103393+1 = 10228565389305891542801
2^103483+1 = 545479572042715043545859
2^103511+1 = 25040709626341385243
2^103511+1 = 266028644197546057
2^103529+1 = 17247595841289024490627
2^103529+1 = 558738320230445777
2^103573+1 = 83752106816548187
2^103591+1 = 13101945417247648130243
2^103591+1 = 3385545668142041249
2^103613+1 = 361381298945183177
2^103651+1 = 2644776401279444978683
2^103657+1 = 110200328776177067
2^103657+1 = 33512316529708162073
2^103681+1 = 1177347314478393859
2^103699+1 = 112440922024027952708141417417
2^103723+1 = 1903675371358138162033387
2^103787+1 = 33992952804543935619217
2^103801+1 = 5759197660361442089227
2^103843+1 = 11967141655671278707
2^103867+1 = 55299272873204625443
2^103963+1 = 2186395828481780070721
2^103969+1 = 12889088730074545475083[/CODE]

 GP2 2019-03-23 01:34

(2^2687383+1)/3/440088720954577 is a probable prime!

(found by Gerbicz cofactor-compositeness test)

 axn 2019-03-23 01:58

104k-106k to t25

[CODE]2^104009+1 = 1871192581503834011
2^104047+1 = 96269581013643540436391843398908212729
2^104059+1 = 131259107234392483
2^104059+1 = 6409667078238699190113050707
2^104107+1 = 2539330234942368851
2^104113+1 = 92355892895182464716057
2^104113+1 = 977096023682922360523
2^104149+1 = 93467949222747501675337
2^104207+1 = 54782143600387471913
2^104233+1 = 3686293185892707889
2^104239+1 = 37654897977588341603
2^104243+1 = 273429663186074456187899
2^104281+1 = 1910383923219218522617
2^104309+1 = 202942920717235763
2^104309+1 = 433544155119286819
2^104309+1 = 91166633410084537
2^104369+1 = 12480736056470620302827
2^104383+1 = 2340396206766468841
2^104383+1 = 3790142996161735727681
2^104393+1 = 4568294215130758594003
2^104459+1 = 1896709605406285217
2^104527+1 = 1743749033293298137313
2^104593+1 = 238697502281749753441
2^104639+1 = 160136958786695677603
2^104651+1 = 1343877698078325746993
2^104707+1 = 1096086468514075321
2^104717+1 = 7713911483328299209
2^104723+1 = 475780492236740978347
2^104773+1 = 595324483368654480782689
2^104801+1 = 73455153023878313
2^104827+1 = 1238706361317363691033
2^104849+1 = 473479104832842835513
2^104911+1 = 30168986625433107481889
2^105071+1 = 10596547420319065566707161
2^105143+1 = 716953504454268455433481
2^105227+1 = 307939348835413649329
2^105229+1 = 149501889050144913299
2^105229+1 = 337048937270886555022097
2^105251+1 = 23670042952788924233
2^105263+1 = 96397860893472781331107
2^105269+1 = 2732993104040786446232267
2^105341+1 = 2895293590136825041
2^105361+1 = 135547441857598335498697
2^105379+1 = 13938500222225012843
2^105389+1 = 19528482455945088809
2^105397+1 = 4685475189623829473
2^105397+1 = 85640378750822682841289
2^105401+1 = 6815728378980739019
2^105407+1 = 130435716363367368859
2^105437+1 = 550810403884361633432607205427
2^105467+1 = 3435144080682427051
2^105503+1 = 1212009856186045021953137
2^105517+1 = 112157983179150330131
2^105529+1 = 280276981591009937
2^105563+1 = 116577049382302330835683
2^105563+1 = 529987267720568561
2^105601+1 = 76525465541632111851482298563
2^105613+1 = 65836151275203530659939
2^105673+1 = 39165181616532437699
2^105701+1 = 1758225672223434707
2^105727+1 = 175239006883723273
2^105767+1 = 1275970129952740950845699
2^105899+1 = 10062777352400448449
2^105899+1 = 75223513642762797778841
2^105913+1 = 202763614753546603
2^105929+1 = 1057788293825747730435652897579[/CODE]

 axn 2019-03-23 01:59

[QUOTE=GP2;511468](2^2687383+1)/3/440088720954577 is a probable prime!

(found by Gerbicz cofactor-compositeness test)[/QUOTE]

:w00t:

 paulunderwood 2019-03-23 05:58

[QUOTE=GP2;511468](2^2687383+1)/3/440088720954577 is a probable prime!

(found by Gerbicz cofactor-compositeness test)[/QUOTE]

Congrats! :toot: My test of it:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^2687383+1)/3/440088720954577" | ../../coding/gwnum/bpsw-2 - 1 2 2687383 1

Testing (2*x)^((n + 1)/2) == -2 (mod n, x^2 - 4*x + 1)...
Likely prime!

real 157m25.395s
user 157m13.504s
sys 0m1.128s
[/CODE]

 DukeBG 2019-03-23 09:07

Wow, very nice, 1.8 mil decimal digits! This should be submitted to [url]http://www.primenumbers.net/prptop/prptop.php[/url]

 paulunderwood 2019-03-23 09:59

[QUOTE=DukeBG;511494]Wow, very nice, 1.8 mil decimal digits! This should be submitted to [url]http://www.primenumbers.net/prptop/prptop.php[/url][/QUOTE]

:ermm: It is ~0.85 million decimal digits.

 GP2 2019-03-23 14:41

[QUOTE=DukeBG;511494]Wow, very nice, 1.8 mil decimal digits! This should be submitted to [url]http://www.primenumbers.net/prptop/prptop.php[/url][/QUOTE]

It's already in their submission queue.

It's only 808968 digits, but there might be a bigger one coming. I paused the double checking for Wagstaff primes at 10 million and will spend the next week or two looking for PRP cofactors for exponents up to either 4 million or 5 million.

 DukeBG 2019-03-23 17:16

i used ln instead of log10 for some reason :redface:

 GP2 2019-03-24 07:51

(2^2860553+1)/3/1528891204123/11630352659013691 is a probable prime!

861084 digits

 paulunderwood 2019-03-24 11:01

[QUOTE=GP2;511643](2^2860553+1)/3/1528891204123/11630352659013691 is a probable prime!

861084 digits[/QUOTE]

Congrats again :toot: My test:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^2860553+1)/3/1528891204123/11630352659013691" | ../../coding/gwnum/bpsw-2 - 1 2 2860553 1

Testing (2*x)^((n + 1)/2) == 2 (mod n, x^2 - 3*x + 1)...
Likely prime!

real 164m27.728s
user 164m3.440s
sys 0m1.708s
[/CODE]

 axn 2019-04-03 03:22

106k-108k to t25

[CODE]2^106103+1 = 528434745495815695003
2^106181+1 = 882817389843510931
2^106291+1 = 4214094046066196902451
2^106297+1 = 7608122844745192838732011
2^106307+1 = 1014342280433172673
2^106331+1 = 4063080438377168147
2^106349+1 = 113343177965880851227
2^106349+1 = 315380352606685591650739
2^106373+1 = 109310838588081107
2^106397+1 = 6102741157152015340180217
2^106411+1 = 716269356910647769
2^106417+1 = 20791960726275498817363
2^106433+1 = 2158415841527756863531
2^106487+1 = 1580356674712022230043
2^106501+1 = 6755457025382142495409
2^106541+1 = 1933915131097764479172481033
2^106619+1 = 26004239725931678605337
2^106621+1 = 10650249812364437046660089
2^106663+1 = 136354946480786641
2^106681+1 = 318832302943679904045552297329
2^106699+1 = 3121662282256221721
2^106727+1 = 136486406157101965771
2^106739+1 = 6424307661703735873
2^106739+1 = 6520808132094406633963
2^106747+1 = 2049377564879734941930139
2^106759+1 = 1354408990826254769443
2^106801+1 = 1535378606998482787
2^106801+1 = 450490719352350617
2^106861+1 = 2615941690498397330873
2^106867+1 = 123404719576082761
2^106877+1 = 27855232546221079547
2^106877+1 = 75978122741932683326620801
2^106903+1 = 23505676485382293308555954299
2^107033+1 = 2570192703246759841
2^107053+1 = 3676985755865732928385289637067
2^107071+1 = 1266829189085797368131
2^107071+1 = 46875124065828911912975537
2^107101+1 = 81810695481933923
2^107183+1 = 27062045882258453347
2^107201+1 = 1356853542512694907
2^107201+1 = 331250585602397119450426073
2^107273+1 = 6605035062044900883811
2^107279+1 = 28819561613691784606057
2^107309+1 = 68473993033306292273
2^107347+1 = 1837315591527374841575826323
2^107377+1 = 157932015461461921917442207633
2^107453+1 = 1276637721707578679527907
2^107507+1 = 240942803930778066121
2^107507+1 = 492909228356815622441
2^107509+1 = 711338047915793743282753
2^107581+1 = 12228659579551150577
2^107581+1 = 23512534601683322723867
2^107599+1 = 479188135440596295553123
2^107621+1 = 13083404513982521401
2^107621+1 = 4375972260198581626081
2^107693+1 = 1438475926758535073
2^107693+1 = 2585644649779141897
2^107699+1 = 675904772163357547
2^107777+1 = 644444939058993203
2^107791+1 = 36624920159639011961
2^107791+1 = 5101136093171270525870897
2^107857+1 = 41865962029800512299
2^107867+1 = 4083593102444233500139091
2^107897+1 = 157668103068411137
2^107923+1 = 3580844104871128769
2^107927+1 = 148117405495878921724480609
2^107951+1 = 21332208885894601237097040683
2^107999+1 = 13050372473856335321537[/CODE]

 axn 2019-04-15 08:07

108k-110k

[CODE]2^108007+1 = 20161650584149961969
2^108007+1 = 78554655680446101913
2^108061+1 = 12873594349810111129
2^108107+1 = 795825355469815511091451
2^108109+1 = 439725587957005366673
2^108127+1 = 22188379941202922393729
2^108131+1 = 15276647725770199673
2^108139+1 = 2582745590063465106349529
2^108139+1 = 5880230261013165697
2^108187+1 = 73834967403236759627
2^108193+1 = 8108249463408458441081
2^108203+1 = 5243445508156841441
2^108211+1 = 3828026832559225291
2^108247+1 = 706008571844699919428441
2^108271+1 = 132351398413842566729
2^108287+1 = 276547846837892081
2^108301+1 = 77794456320986287995163
2^108359+1 = 2321863511288971451
2^108421+1 = 389528342943562676514601
2^108439+1 = 16645832636432230064582569
2^108457+1 = 213000604936177335493967017
2^108497+1 = 22176817467150675209011
2^108499+1 = 167767922698194462940753
2^108499+1 = 2210900571991762993
2^108499+1 = 28718448814483699418150033
2^108533+1 = 670431165743914974521
2^108541+1 = 75106846053782872112552955169
2^108557+1 = 431012264001552592756318619
2^108649+1 = 72851702844603797194153
2^108751+1 = 82171099094885569
2^108769+1 = 205164869773612811
2^108769+1 = 52431431859034698257
2^108803+1 = 103464599754667104757945763
2^108863+1 = 72846067235810690977
2^108881+1 = 40935401561223537859723
2^108893+1 = 2626281013519919587163
2^108907+1 = 26137559760811714331
2^108907+1 = 597560978586734411
2^108967+1 = 217548277489346988689
2^109073+1 = 1858350610137700102721963
2^109103+1 = 108282670444980457
2^109159+1 = 45567038236224260162777
2^109159+1 = 5025984704147602251163
2^109159+1 = 900460656306737968523129
2^109169+1 = 908161286108682336942161
2^109199+1 = 738940767863002777951601
2^109297+1 = 290736326447392513
2^109357+1 = 266179990494217070809
2^109367+1 = 27375331870011563371
2^109391+1 = 42551120467296138617
2^109453+1 = 32272430192962832503445761
2^109469+1 = 371820300609980371
2^109481+1 = 692863390436865079171
2^109517+1 = 17566759943397747083
2^109537+1 = 21486498333611001898651
2^109567+1 = 4211062626325953667
2^109579+1 = 34026820129942162979
2^109589+1 = 1155305061559714845882904729
2^109639+1 = 21058023086293012601
2^109639+1 = 2499302862809748696739
2^109663+1 = 4951583686483024267
2^109663+1 = 5926673484517064963491
2^109841+1 = 5820117122207879398318451
2^109843+1 = 2480220549512587932097
2^109883+1 = 147043337556706027750129
2^109897+1 = 37304198443836366559817
2^109903+1 = 260450070667464187
2^109919+1 = 765680460264949211
2^109937+1 = 792462902650816057
2^109961+1 = 2034372804488913601[/CODE]

 axn 2019-05-09 05:10

110k-112k

[CODE]2^110051+1 = 65228366464044326779
2^110161+1 = 29188102365665319058167259
2^110291+1 = 3867434383076500819841
2^110321+1 = 75922143799451987
2^110339+1 = 22777693856762463842081
2^110441+1 = 12058958783275929164659
2^110543+1 = 2245836194166106499
2^110557+1 = 7312248712686045017
2^110569+1 = 162942677419243265472672011
2^110569+1 = 294586778266791446627
2^110597+1 = 12955085535495184121
2^110597+1 = 135361252094163577
2^110641+1 = 618633569908451378627
2^110681+1 = 145331465490016961
2^110681+1 = 1939403983673219889971
2^110711+1 = 1023237052000159259
2^110711+1 = 146844872984198039570991481
2^110729+1 = 491781115198744036507
2^110819+1 = 1935823380424571697631280881
2^110899+1 = 509075540962889466017
2^110909+1 = 770432194150109347
2^110917+1 = 727651461392280043
2^110923+1 = 65476933834210720003425538913
2^110947+1 = 50771322887957337344353
2^111029+1 = 7182586703247506009
2^111103+1 = 663975330197147201531
2^111109+1 = 1729484624185407101618153
2^111121+1 = 74991590832739697
2^111143+1 = 66722490593050649190529
2^111211+1 = 72192650932622514067
2^111229+1 = 157517200252763339
2^111269+1 = 76602908006822468977
2^111301+1 = 21221563560086898313
2^111341+1 = 516844719540913647631468519961
2^111509+1 = 3725609409631134713
2^111509+1 = 85233935575689347
2^111577+1 = 692020081728450407321
2^111599+1 = 245393663959188883
2^111599+1 = 724025586915157911066899
2^111623+1 = 115937493150701947
2^111623+1 = 203103300969769354009
2^111641+1 = 24823417013975832649
2^111697+1 = 185828394324071417
2^111697+1 = 2683079450165557869398613187
2^111721+1 = 20123824899063272490598753
2^111781+1 = 28189374052921757085915257
2^111791+1 = 9751189493994636003971
2^111821+1 = 10416389967281467681
2^111821+1 = 26666212077327574650330739
2^111833+1 = 106303413937867067
2^111833+1 = 18714757354829626633
2^111893+1 = 6844003901836848067
2^111919+1 = 14039282793911716435841
2^111949+1 = 103606711690134381560233673
2^111949+1 = 16586205647299856179
2^111949+1 = 79999745460163651
2^111959+1 = 2682564874505934521
2^111977+1 = 9432834465383409131[/CODE]

 GP2 2019-05-15 19:55

[M]M268,435,459[/M] (exponent = 2[SUP]28[/SUP]+3) has been found to be composite by PRP-3 test.

The Wagstaff number with this same exponent has a small factor (414099276471761).

The "[URL="http://mprime.s3-website.us-west-1.amazonaws.com/new_mersenne_conjecture.html"]new Mersenne conjecture[/URL]", which is overwhelmingly likely to be trivially true, thus remains unrefuted.

 GP2 2019-05-26 22:42

[QUOTE=axn;500380]You can take 3k onwards to t40 (using P95 + GMP-ECM - just P95 alone would not be most efficient).[/QUOTE]

[QUOTE=GP2;500406]OK, let's do that.[/QUOTE]

I have ECM'd to t=40 the Wagstaff range from 3k to 5k.

There were 40 new factors of 35 different exponents. Only two exponents out of the 35 were previously unfactored. No new PRP cofactors resulted.

I'm continuing past 5k now. Only two cores are being used for this, so it's going slowly.

I'm also doing the 2k to 3k range to t=45. I've almost reached 2.3k, only p=2297 is still pending. There were 2 new factors of 2 different exponents. One of the 2 exponents was previously unfactored. No new PRP cofactors have resulted.

 axn 2019-06-14 03:42

112k-114k

[CODE]2^112031+1 = 1910979345058022183326667
2^112103+1 = 83515512541366176140803
2^112139+1 = 5815743905218852233163
2^112199+1 = 2010215840685274597801
2^112199+1 = 786323718506582866249
2^112213+1 = 106497029548103220408449
2^112213+1 = 251422755955621961
2^112289+1 = 12512701387828660438033
2^112303+1 = 8311350638547158641
2^112397+1 = 2399240796804037893721132931
2^112459+1 = 375831592044995414089
2^112459+1 = 776445049666235026096699
2^112559+1 = 2794720627981248137
2^112571+1 = 49526001393468280031081
2^112573+1 = 636825460050432035150256611
2^112577+1 = 27551115531353237897
2^112621+1 = 1013589232168271434781929
2^112741+1 = 11668085678799635206529
2^112757+1 = 1261271778646931314310881
2^112799+1 = 20363535440517925993
2^112831+1 = 553025594888740113336467
2^112843+1 = 14887446047818700003
2^112843+1 = 1816520364952020859051
2^112859+1 = 2214390484782040843
2^112927+1 = 363455995504734793
2^112927+1 = 54000116293238248297
2^112951+1 = 12695680452667613129
2^112967+1 = 4018332491352410771
2^112979+1 = 188348147492137236527331553
2^112997+1 = 1824913074235208731
2^113011+1 = 2625547572826243961057
2^113023+1 = 21847818142372348880449
2^113023+1 = 86839986899358725835245929
2^113039+1 = 2015829528724557883
2^113039+1 = 2995800831811614859
2^113123+1 = 1643110379745335948319577
2^113143+1 = 69598053853807666387
2^113147+1 = 31318095488042954868313843
2^113147+1 = 6083084761062748733339
2^113149+1 = 1152833489823258508548560267
2^113149+1 = 8726751543730916009
2^113153+1 = 184455589859040989932097
2^113159+1 = 311118349570646689
2^113173+1 = 3268839850336231086269176698080107729
2^113173+1 = 918683847655298504676157788707
2^113189+1 = 487068254046171073
2^113213+1 = 59118312964102575769
2^113233+1 = 2720674525064101486628603
2^113287+1 = 2186655841902836641
2^113341+1 = 4489383701941289278750459
2^113341+1 = 5403379610851755529
2^113381+1 = 4635091610159983523765131
2^113383+1 = 167889695306414171
2^113417+1 = 29393519805369961673039899
2^113453+1 = 654252952523696921
2^113467+1 = 246374506417924394208427
2^113489+1 = 471672108093873191419
2^113501+1 = 76734603980709449891
2^113513+1 = 109626760389090963997819
2^113513+1 = 540575926005891362729
2^113537+1 = 143374729891998821507
2^113537+1 = 35290787662497113737
2^113539+1 = 543484110245446406177
2^113647+1 = 7270305779257350739841
2^113657+1 = 2375398635154102731999803
2^113683+1 = 4274281119942093092033
2^113719+1 = 154895530205772046800441427
2^113723+1 = 3034004502637956329
2^113837+1 = 147487993204082546009
2^113837+1 = 1493008605813853238113
2^113891+1 = 63942026456511010985131
2^113933+1 = 246570918531443273
2^113933+1 = 2546221246474770217
2^113933+1 = 563775020565030528315851
2^113947+1 = 2732539978758883817
2^113947+1 = 3297119904032099079089
2^113947+1 = 748152928956257484458707
2^113983+1 = 9013319653109434657[/CODE]

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