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

TheJudger 2018-08-12 11:43

Hi,

[QUOTE=diep;492377]Another difference seems the factoring. Trial Factoring, but i lack hard data of Mersenne to compare it with, seems more effective for Wagstaff than it is for Mersenne.

Some researcher who wants to take this important unpaid job on himself might be able to officially determine that. I just posted here a gutfeeling.

Though there might be a simple explanation for it that has to do with the spread of primes there. Because we divide by 3, maybe it is the case there is less Wagstaffs between [n and 2n].

As a result TF seemingly is far more effective so it would be possible to search Wagstaff deeper than Mersenne using the same horse power. [/QUOTE]

I would be careful with that. While the following it [B]not[/B] a proof you have to think about it:
For mersenne numbers there is a chance of 1/x for a mersenne number to have a factor in the range 2[SUP]x[/SUP] and 2[SUP]x+1[/SUP]. The product of all factors is the factored number itself thus the sum of the "sizes" of the factors must match the "size" of the factored number.
1/1 * log[SUB]2[/SUB](2[SUP]1[/SUP]) + 1/2 * log[SUB]2[/SUB](2[SUP]2[/SUP]) + 1/3 * log[SUB]2[/SUB](2[SUP]3[/SUP]) + [...] + 1/p * log[SUB]2[/SUB](2[SUP]p[/SUP]) = log[SUB]2[/SUB](2[SUP]p[/SUP])
1 + 1 + 1 + [...] + 1 = p (there is p times a "1" on the left side)

So when you say there are more smaller factors for a wagstaff number compared to a mersenne number you have to explain why there are less bigger factors for a wagstaff number at the same time.

Ofc. not a proof and not correct because factors aren't fixed size but ranges...


Oliver

GP2 2018-08-12 23:57

(2^823337+1)/(3*362268281) is a PRP




In the [URL="http://mersenneforum.org/showthread.php?t=23462"]formulation of the Gerbicz cofactor-compositeness test[/URL], having [c]w < d[/c] is a necessary but not sufficient condition for the cofactor to be prime. But so far, every candidate that passes that test also passes the probable-prime tests, as long as the prior conditions [c]t<p[/c] and [c]d<2^t[/c] are also met. I am using t=2048 bits, so these last two conditions are never an issue.

I wonder if it is possible to have a cofactor where [c]w < d[/c] but it still fails the probabilistic Fermat primality test? How common would that be?

paulunderwood 2018-08-13 00:26

[QUOTE=GP2;493752](2^823337+1)/(3*362268281) is a PRP




In the [URL="http://mersenneforum.org/showthread.php?t=23462"]formulation of the Gerbicz cofactor-compositeness test[/URL], having [c]w < d[/c] is a necessary but not sufficient condition for the cofactor to be prime. But so far, every candidate that passes that test also passes the probable-prime tests, as long as the prior conditions [c]t<p[/c] and [c]d<2^t[/c] are also met. I am using t=2048 bits, so these last two conditions are never an issue.

I wonder if it is possible to have a cofactor where [c]w < d[/c] but it still fails the probabilistic Fermat primality test? How common would that be?[/QUOTE]

Congrats! My test:

[CODE] time ./pfgw64 -k -f0 -od -q"(2^823337+1)/(3*362268281)" | ../../coding/gwnum/hybrid - 1 2 823337 1

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

real 5m33.658s
user 9m22.076s
sys 1m4.816s
[/CODE]

GP2 2018-08-13 02:58

Generalized repunit conjecture
 
Based on the [URL="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0906&L=NMBRTHRY&P=R295&1=NMBRTHRY&9=A&J=on&d=No+Match%3BMatch%3BMatches&z=4"]generalized repunit conjecture[/URL] by Paul Bourdelais, we should not expect exactly the same frequency for Wagstaff primes as for Mersenne primes.

The parameter G (in the linked page) is 1/e^gamma = 0.56145948... where Euler-Mascheroni gamma ≈ 0.5772, and the average ratio of exponents of successive Mersenne primes should be the familiar 2[sup]G[/sup] ≈ 1.47576...

And the same should be true for any prime repunits in any positive base b (see below for background info).

But the linked page makes the argument that for negative bases b (e.g., for Wagstaffs), due to the exclusion of the even prime p = 2, the applicable value is G ≈ 0.47, at least for p less than 1M, which implies an average ratio of exponents of successive Wagstaff primes of 2[sup]G[/sup] ≈ 1.385...


Mersenne primes are prime repunits in base 2 (binary representation = ...1111111111)

Wagstaff primes are prime repunits in base negative 2 (binary representation = ...1010101011)

The generalized repunit primes are primes of the form

R[sub]p[/sub](b) = (b[sup]p[/sup] − 1) / (b − 1)

With b=2 for Mersennes it's (2[sup]p[/sup] − 1) / 1

With b=−2 for Wagstaffs it's (−2[sup]p[/sup] − 1) / −3 and for odd primes p this is (2[sup]p[/sup] + 1) / 3

axn 2018-08-13 03:00

[QUOTE=GP2;493752]I wonder if it is possible to have a cofactor where [c]w < d[/c] but it still fails the probabilistic Fermat primality test? How common would that be?[/QUOTE]
Yes. Consider a random t-bit integer. What is the probability that the most-signifcant t-log[SUB]2[/SUB](d) bits are all zero? That's your probability that a composite number will generate a residue < d. The more additional bits you keep, the less likely this will be.

GP2 2018-08-13 03:22

The [URL="https://en.wikipedia.org/wiki/Repunit"]Wikipedia page for "Repunit"[/URL] has a lot of info about repunit primes in various bases b.

It also has [URL="https://en.wikipedia.org/wiki/Repunit#The_generalized_repunit_conjecture"]a section on the generalized repunit conjecture[/URL], with an unusual formula.

(here is [URL="https://en.wikipedia.org/w/index.php?title=Repunit&oldid=853507603#The_generalized_repunit_conjecture"]the link to the current version[/URL], in case it gets edited in the future.

There is no explanation for this formula, and of course since it's Wikipedia it could be complete nonsense.

In any case, the number of base b repunit primes less than N is supposedly:

(log(N) + m * log(2) * log(log(N)) + 1/sqrt(N) - delta) * e^gamma / (log (abs(b))

Here log is the natural logarithm, gamma is the Euler-Mascheroni constant, e is the base of natural logs, etc. And note N is the actual number (e.g., 2[SUP]p[/SUP]−1) rather than the exponent.

However the parameters of interest are:

"delta", which is 1 for positive b and 1.6 for negative b (no explanation given)

"m" is the largest natural number such that −b is a 2[SUP]m−1[/SUP]th power


Since b = 2 for Mersenne, I don't know how to interpret the definition of "m" for it

But for b = −2 for Wagstaff, so m = 2

For large N, the log(N) term dominates all the others.

But for smaller N, the term involving m should make a contribution. So you might expect Wagstaff primes to be more frequent at the small end.


But again, this formula could be nonsense. It could have been added to the Wikipedia page by anyone, and might not be consistent with the actual generalized repunit conjecture as formulated by Paul Bourdelais.

In any case, I don't think we have any explanation for the anomalously large gaps between the largest known Wagstaff primes, which are well above average.

axn 2018-08-18 10:01

(2^10597+1)/3 = 302650321 · 134674978728307 · 27900494994833595768916409 · PRP3142

paulunderwood 2018-08-18 10:21

[QUOTE=axn;494124](2^10597+1)/3 = 302650321 · 134674978728307 · 27900494994833595768916409 · PRP3142[/QUOTE]

Congrats. My quick test:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^10597+1)/3/302650321/134674978728307/27900494994833595768916409" | ../../coding/gwnum/hybrid - 1 2 10597 1

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

real 0m0.112s
user 0m0.172s
sys 0m0.008s
[/CODE]

This is well within reach of a Primo proof :smile:

GP2 2018-08-18 14:17

[QUOTE=axn;494124](2^10597+1)/3 = 302650321 · 134674978728307 · 27900494994833595768916409 · PRP3142[/QUOTE]

That largest factor was previously unknown to me. Do you have any more?

I have a merged Wagstaff factors list based on contributions from 2013 by ATH and others. Still missing potential contributions from Jeff Gilchrist and Ryan Propper, so I haven't tried to publish it yet.

In any case, based on the factors I know and the testing I've done so far, and [STRIKE]not[/STRIKE] including this new one, the following Wagstaff exponents are fully-factored or probably-fully-factored. I'm currently testing the 1M to 2M range.

[CODE]
every exponent under 1033
1039
1049
1051
1061
1069
1093
1103
1117
1171
1181
1193
1217
1229
1237
1277
1279
1447
1453
1459
1607
1609
1613
1627
1667
1721
1861
1867
1873
1951
1973
1979
1999
2017
2039
2063
2137
2161
2239
2411
2543
2579
2633
2647
2707
3061
3169
3329
3613
3877
3967
4481
4483
4567
4651
5413
6163
6701
6947
7417
8167
8329
8387
8849
9461
9803
10343
10597
11411
12497
14489
15313
20201
21613
32369
41269
80819
83423
85517
91159
161683
257869
343933
364513
610289
685739
823337
[/CODE]

axn 2018-08-18 16:58

[QUOTE=GP2;494137]That largest factor was previously unknown to me. Do you have any more?[/QUOTE]
I am running t30 on exponents starting from 10500 (Why there? Eyeballing the factordb, that looked to be where deep factoring was not done). I have 7 new factors so far (including the one above). Once I am done with the batch, I'll post them here, but of course they're already available in factordb. I'll keep going till I lose interest.

GP2 2018-08-18 19:29

I made a little webpage with some downloadable files related to Wagstaff numbers: [url]http://mprime.s3-website.us-west-1.amazonaws.com/[/url]

These files include 2048-bit residues for exponents from 0M to 1M, and all factors that I currently know about, and a small Python script for doing the rapid Gerbicz cofactor-compositeness test.

In the residues file, all prime exponents are included, whether or not they have known prime factors.

All of these residues were calculated using only "3" for the list of factors. In the old days, that would make no sense, since you'd have to redo the PRP cofactor test every time a new factor was discovered. But now you just do the cofactor-compositeness test and get the answer in a few seconds.

paulunderwood 2018-08-18 19:48

Perhaps one of the super mods can create the link to your site underneath "Wagstaff PRP Search" on MF.

Batalov 2018-08-18 20:05

[QUOTE=paulunderwood;494157]Perhaps [COLOR=DarkRed]one of the super mods[/COLOR] can create the link to your site underneath "Wagstaff PRP Search" on MF.[/QUOTE]
Write PM to Mike. That's only Mike's prerogative.

paulunderwood 2018-08-18 20:09

[QUOTE=Batalov;494162]Write PM to Mike. That's only Mike's prerogative.[/QUOTE]

Done! :smile:

GP2 2018-08-18 20:56

[QUOTE=paulunderwood;494163]Done! :smile:[/QUOTE]

Sorry for the trouble, but I decided to move the Wagstaff stuff into a subdirectory, so:

[url]http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/[/url]

That way, the home page could be used for additional stuff in the future...

paulunderwood 2018-08-18 21:05

[QUOTE=GP2;494167]Sorry for the trouble, but I decided to move the Wagstaff stuff into a subdirectory, so:

[url]http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/[/url]

That way, the home page could be used for additional stuff in the future...[/QUOTE]

"Exponents of known Wagstaff primes": Put a "(probable)" in from of "primes". Not all have been proved prime. [url]http://primes.utm.edu/top20/page.php?id=67[/url] shows the largest is for p = 83339.

axn 2018-08-20 02:38

[QUOTE=axn;494147]Once I am done with the batch, I'll post them here[/QUOTE]
Factors found in 10500-11000 range. Continuing on to 11000-11500.
[CODE]2^10513+1 has a factor: 558850357800061263555001 (ECM curve 100, B1=250000, B2=25000000)
2^10597+1 has a factor: 27900494994833595768916409 (ECM curve 60, B1=250000, B2=25000000)
2^10601+1 has a factor: 2099904243015017007033617 (ECM curve 27, B1=250000, B2=25000000)
2^10601+1 has a factor: 41575688406606520910981619667 (ECM curve 109, B1=250000, B2=25000000)
2^10651+1 has a factor: 2134589112965811282457 (ECM curve 13, B1=250000, B2=25000000)
2^10657+1 has a factor: 45041555878821505356467 (ECM curve 26, B1=250000, B2=25000000)
2^10709+1 has a factor: 41425034801610179 (ECM curve 2, B1=250000, B2=25000000)
2^10729+1 has a factor: 1095893574000877512503136952657 (ECM curve 73, B1=250000, B2=25000000)
2^10739+1 has a factor: 3255387377916397764176273 (ECM curve 13, B1=250000, B2=25000000)
2^10771+1 has a factor: 33882722360407647786347 (ECM curve 1, B1=250000, B2=25000000)
2^10789+1 has a factor: 14139483905607252493155733243 (ECM curve 41, B1=250000, B2=25000000)
2^10859+1 has a factor: 2809519974292587762377009 (ECM curve 36, B1=250000, B2=25000000)
2^10861+1 has a factor: 67174765804253243 (ECM curve 3, B1=250000, B2=25000000)
2^10883+1 has a factor: 19073771355362076504470660219 (ECM curve 155, B1=250000, B2=25000000)
2^10883+1 has a factor: 19452747127355996044349636366680216273 (ECM curve 137, B1=250000, B2=25000000)
2^10889+1 has a factor: 15538521494997703956251 (ECM curve 54, B1=250000, B2=25000000)
2^10889+1 has a factor: 19171773405633598965775513 (ECM curve 111, B1=250000, B2=25000000)
2^10937+1 has a factor: 6273989859709247143821713 (ECM curve 32, B1=250000, B2=25000000)
2^10973+1 has a factor: 66253674245601831966227 (ECM curve 12, B1=250000, B2=25000000)
2^10979+1 has a factor: 45970923917705027 (ECM curve 4, B1=250000, B2=25000000)
2^10993+1 has a factor: 2275949879439998829440830129 (ECM curve 18, B1=250000, B2=25000000)
[/CODE]

GP2 2018-08-20 09:10

[QUOTE=axn;494257]Factors found in 10500-11000 range. Continuing on to 11000-11500.[/QUOTE]

Great stuff.

Currently I'm maintaining the list of factors as a flat file, with command-line utilities. It probably should be a database at some point, with residues and factors.

The structure of that database would no doubt be very similar to what already exists for Mersenne numbers, other than the residues being 2048 bits. I don't suppose mersenne.org or mersenne.ca would want to host this data?

PS, be sure to skip 19937 if you ever get to it, it's already been ECM'd to > t=50 without success, according to the site linked at the bottom of [URL="http://mprime.s3-website.us-west-1.amazonaws.com/new_mersenne_conjecture.html"]this page[/URL].

axn 2018-08-23 10:59

11000-11500 completed with 17 new factors. No PRPs though.
[CODE]2^11003+1 has a factor: 4685815055513847038323 (ECM curve 8, B1=250000, B2=25000000)
2^11027+1 has a factor: 23807519596109758628659433 (ECM curve 58, B1=250000, B2=25000000)
2^11047+1 has a factor: 1251837532102748869378489535233 (ECM curve 256, B1=250000, B2=25000000)
2^11059+1 has a factor: 513048812645907465359182073707 (ECM curve 47, B1=250000, B2=25000000)
2^11113+1 has a factor: 204883071601667227512940182947 (ECM curve 483, B1=250000, B2=25000000)
2^11117+1 has a factor: 21817821571538620561 (ECM curve 1, B1=250000, B2=25000000)
2^11117+1 has a factor: 45057036520415605787801473 (ECM curve 82, B1=250000, B2=25000000)
2^11369+1 has a factor: 6344134703214758363 (ECM curve 1, B1=250000, B2=25000000)
2^11149+1 has a factor: 1315517726921100747571 (ECM curve 6, B1=250000, B2=25000000)
2^11149+1 has a factor: 588015852062690954378491 (ECM curve 24, B1=250000, B2=25000000)
2^11161+1 has a factor: 2949683386088436883 (ECM curve 9, B1=250000, B2=25000000)
2^11399+1 has a factor: 106324343838177712742657 (ECM curve 12, B1=250000, B2=25000000)
2^11171+1 has a factor: 33775951166577307764073 (ECM curve 21, B1=250000, B2=25000000)
2^11437+1 has a factor: 364539853712621516689 (ECM curve 8, B1=250000, B2=25000000)
2^11437+1 has a factor: 438901061511190129278741121 (ECM curve 314, B1=250000, B2=25000000)
2^11197+1 has a factor: 867780839678688375573501497 (ECM curve 15, B1=250000, B2=25000000)
2^11239+1 has a factor: 194953394901165635556414731 (ECM curve 337, B1=250000, B2=25000000)
2^11243+1 has a factor: 345127813705251122046213787 (ECM curve 78, B1=250000, B2=25000000)
2^11471+1 has a factor: 1808263130555951119335347 (ECM curve 24, B1=250000, B2=25000000)
2^11483+1 has a factor: 13780428516626567566675236851 (ECM curve 214, B1=250000, B2=25000000)
2^11483+1 has a factor: 48174113181102736591723769 (ECM curve 98, B1=250000, B2=25000000)
[/CODE]

However, the next range 11500-12000 immediately brought this:
[CODE]ECM found a factor in curve #509, stage #2
Sigma=2010169538613608, B1=250000, B2=25000000.
2^11503+1 has a factor: 172614806491354681945557260113 (ECM curve 509, B1=250000, B2=25000000)
Cofactor is a probable prime!
[/CODE]
Thus, (2^11503+1)/3 = 9485367850806014107 · 172614806491354681945557260113 · PRP3415

ET_ 2018-08-23 12:11

[QUOTE=axn;494517]
Thus, (2^11503+1)/3 = 9485367850806014107 · 172614806491354681945557260113 · PRP3415[/QUOTE]

I guess the PRP can easily be tested with Primo...

paulunderwood 2018-08-23 13:53

[QUOTE=ET_;494521]I guess the PRP can easily be tested with Primo...[/QUOTE]

In the meantime:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^11503+1)/3/9485367850806014107/172614806491354681945557260113" | ../../coding/gwnum/hybrid - 1 2 11503 1

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

real 0m0.122s
user 0m0.224s
sys 0m0.008s
[/CODE]

[CODE]./pfgw64 -k -f0 -tc -q"(2^11503+1)/3/9485367850806014107/172614806491354681945557260113"
Primality testing (2^11503+1)/3/9485367850806014107/172614806491354681945557260113 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 8+sqrt(13)
(2^11503+1)/3/9485367850806014107/172614806491354681945557260113 is Fermat and Lucas PRP! (0.5371s+0.0104s)
[/CODE]

Congrats axn! :tu:

axn 2018-08-25 15:49

Factors from 11500-12000
[CODE]2^11503+1 has a factor: 172614806491354681945557260113 (ECM curve 509, B1=250000, B2=25000000)
2^11549+1 has a factor: 34703384064927652099 (ECM curve 10, B1=250000, B2=25000000)
2^11579+1 has a factor: 306722676915944303956238411 (ECM curve 94, B1=250000, B2=25000000)
2^11579+1 has a factor: 54620416271184620865539661238739 (ECM curve 109, B1=250000, B2=25000000)
2^11617+1 has a factor: 58373376055644455317354147 (ECM curve 49, B1=250000, B2=25000000)
2^11617+1 has a factor: 7390894586030876545552674881 (ECM curve 279, B1=250000, B2=25000000)
2^11633+1 has a factor: 29524655697455332769 (ECM curve 39, B1=250000, B2=25000000)
2^11677+1 has a factor: 7412795431880652924805627 (ECM curve 53, B1=250000, B2=25000000)
2^11699+1 has a factor: 617822826591146233 (ECM curve 1, B1=250000, B2=25000000)
2^11701+1 has a factor: 55969492654337699 (ECM curve 5, B1=250000, B2=25000000)
2^11719+1 has a factor: 46769692899921148775974141889507 (ECM curve 270, B1=250000, B2=25000000)
2^11789+1 has a factor: 1643532758066793714880922993 (ECM curve 143, B1=250000, B2=25000000)
2^11801+1 has a factor: 288335665894071795641 (ECM curve 29, B1=250000, B2=25000000)
2^11801+1 has a factor: 3303013919063025724130297591998121 (ECM curve 23, B1=250000, B2=25000000)
2^11833+1 has a factor: 1222062551920076191116091 (ECM curve 79, B1=250000, B2=25000000)
2^11867+1 has a factor: 7789562648034705026391361 (ECM curve 169, B1=250000, B2=25000000)
2^11939+1 has a factor: 313063798567456396249 (ECM curve 116, B1=250000, B2=25000000)
2^11959+1 has a factor: 129524215904316555400937483 (ECM curve 8, B1=250000, B2=25000000)
2^11959+1 has a factor: 23865858116434345003645527851 (ECM curve 328, B1=250000, B2=25000000)
[/CODE]

axn 2018-08-28 02:48

12000-12500
[CODE]2^12043+1 has a factor: 931316532448721355907 (ECM curve 8, B1=250000, B2=25000000)
2^12071+1 has a factor: 5363577254448290441090123137 (ECM curve 70, B1=250000, B2=25000000)
2^12101+1 has a factor: 58524707531213140003 (ECM curve 19, B1=250000, B2=25000000)
2^12107+1 has a factor: 4268182528348577280510505097 (ECM curve 406, B1=250000, B2=25000000)
2^12109+1 has a factor: 117954995881886494047443522370529 (ECM curve 42, B1=250000, B2=25000000)
2^12119+1 has a factor: 3958582688037701051 (ECM curve 2, B1=250000, B2=25000000)
2^12203+1 has a factor: 25967591817423371 (ECM curve 2, B1=250000, B2=25000000)
2^12203+1 has a factor: 32199660881088987821329719937 (ECM curve 152, B1=250000, B2=25000000)
2^12211+1 has a factor: 92467278959442571049 (ECM curve 7, B1=250000, B2=25000000)
2^12227+1 has a factor: 15330146197583947 (ECM curve 31, B1=250000, B2=25000000)
2^12239+1 has a factor: 36392066836960281195603567971 (ECM curve 145, B1=250000, B2=25000000)
2^12241+1 has a factor: 19297234102386238576716011 (ECM curve 114, B1=250000, B2=25000000)
2^12253+1 has a factor: 24795447267048647003251 (ECM curve 16, B1=250000, B2=25000000)
2^12277+1 has a factor: 1589828583281008307 (ECM curve 2, B1=250000, B2=25000000)
2^12323+1 has a factor: 5694497990681201586721 (ECM curve 13, B1=250000, B2=25000000)
2^12343+1 has a factor: 16221640341669457211921 (ECM curve 35, B1=250000, B2=25000000)
2^12373+1 has a factor: 383919305853053677937 (ECM curve 1, B1=250000, B2=25000000)
2^12377+1 has a factor: 1627307486652507739834019 (ECM curve 23, B1=250000, B2=25000000)
2^12473+1 has a factor: 17319169916767373818571 (ECM curve 19, B1=250000, B2=25000000)
2^12479+1 has a factor: 29537777610278615971 (ECM curve 15, B1=250000, B2=25000000)
2^12487+1 has a factor: 75825154947583937249 (ECM curve 3, B1=250000, B2=25000000)
[/CODE]

GP2 2018-08-30 16:49

[QUOTE=ET_;494521]I guess the PRP can easily be tested with Primo...[/QUOTE]

The cofactor for Wagstaff 11503 was indeed Primo certified on the same day you posted.

But if anyone's interested, the following PRP cofactors of Wagstaff composites are still uncertified:

15313
20201
21613
32369
41269
and then nothing until:
80819
83423
85517

Meanwhile, all Wagstaff primes up to and including exponent 83339 have been certified, but exponent 42737 used a non-Primo certification method, and thus there is no certificate at FactorDB.

axn 2018-08-30 17:23

[QUOTE=GP2;494952]but exponent 42737 used a non-Primo certification method, and thus there is no certificate at FactorDB.[/QUOTE]

I was wondering... Since it is an ECPP certificate, is it somehow possible to just reformat it to make it Primo-compatible? It'd be a shame if we had to redo the whole thing ...

GP2 2018-08-30 21:19

[QUOTE=axn;494954]I was wondering... Since it is an ECPP certificate, is it somehow possible to just reformat it to make it Primo-compatible? It'd be a shame if we had to redo the whole thing ...[/QUOTE]

I believe the answer is no.

But in any case, here is a page with a link to download the certificate: [url]https://primes.utm.edu/primes/page.php?id=82071#user[/url]

GP2 2018-08-31 21:57

Here are the Wagstaff prime exponents which are also Sophie Germain primes:

[CODE]
3
5
11
23
191
3539
10691
83339
4031399
13347311
[/CODE]

It's interesting that two of the three largest known Wagstaff primes have Sophie-Germain-prime exponents (the exception is 13372531).

For Mersenne primes, the list is (OEIS sequence [URL="https://oeis.org/A065406"]A065406[/URL]):

[CODE]
2, 3, 5, 89, 9689, 21701, 859433, 43112609
[/CODE]

axn 2018-09-01 01:56

(2^12829+1)/3 = 209172250126410856422810178313 · PRP3833

paulunderwood 2018-09-01 05:40

Congrats axn!

[CODE]time ./pfgw64 -k -f0 -od -q"(2^12829+1)/3/209172250126410856422810178313" | ../../coding/gwnum/hybrid - 1 2 12829 1

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

real 0m0.135s
user 0m0.204s
sys 0m0.004s
[/CODE]

axn 2018-09-01 15:50

12500-13000
[CODE]2^12527+1 has a factor: 495985175665792988375165177 (ECM curve 290, B1=250000, B2=25000000)
2^12539+1 has a factor: 316348113508828547219 (ECM curve 29, B1=250000, B2=25000000)
2^12541+1 has a factor: 608805974640112745209872699899 (ECM curve 190, B1=250000, B2=25000000)
2^12547+1 has a factor: 71351892535746316766504387521 (ECM curve 363, B1=250000, B2=25000000)
2^12553+1 has a factor: 3671587828174324814065091393 (ECM curve 501, B1=250000, B2=25000000)
2^12601+1 has a factor: 444966945171977 (ECM curve 2, B1=250000, B2=25000000)
2^12613+1 has a factor: 14619793634422449392097149371 (ECM curve 228, B1=250000, B2=25000000)
2^12613+1 has a factor: 48241955162558857769 (ECM curve 1, B1=250000, B2=25000000)
2^12619+1 has a factor: 2768447202637809330906409 (ECM curve 153, B1=250000, B2=25000000)
2^12641+1 has a factor: 7742855471159370226026448568897 (ECM curve 480, B1=250000, B2=25000000)
2^12641+1 has a factor: 7877749770534103067 (ECM curve 19, B1=250000, B2=25000000)
2^12689+1 has a factor: 346236779981776209481 (ECM curve 7, B1=250000, B2=25000000)
2^12689+1 has a factor: 668917618997656321289 (ECM curve 5, B1=250000, B2=25000000)
2^12703+1 has a factor: 244967263716299761745918559654043 (ECM curve 391, B1=250000, B2=25000000)
2^12703+1 has a factor: 25097622545339107451 (ECM curve 2, B1=250000, B2=25000000)
2^12721+1 has a factor: 104521770109653278879086116333571 (ECM curve 258, B1=250000, B2=25000000)
2^12721+1 has a factor: 3291668563782247219135339883 (ECM curve 2, B1=250000, B2=25000000)
2^12721+1 has a factor: 4903609749360983212707931 (ECM curve 29, B1=250000, B2=25000000)
2^12763+1 has a factor: 7200433146311431601 (ECM curve 1, B1=250000, B2=25000000)
2^12781+1 has a factor: 356918493274201597652356067 (ECM curve 99, B1=250000, B2=25000000)
2^12809+1 has a factor: 20983819350213541771 (ECM curve 18, B1=250000, B2=25000000)
2^12829+1 has a factor: 209172250126410856422810178313 (ECM curve 309, B1=250000, B2=25000000)
2^12853+1 has a factor: 27072593005625348544947552569 (ECM curve 347, B1=250000, B2=25000000)
2^12889+1 has a factor: 454838553245679062310449 (ECM curve 151, B1=250000, B2=25000000)
2^12899+1 has a factor: 389039635887266774569 (ECM curve 31, B1=250000, B2=25000000)
2^12899+1 has a factor: 41819200638887898467 (ECM curve 3, B1=250000, B2=25000000)
2^12917+1 has a factor: 3976395356166805139 (ECM curve 4, B1=250000, B2=25000000)
[/CODE]

axn 2018-09-05 10:54

13000-13500
[CODE]2^13007+1 has a factor: 10156558000626213932521 (ECM curve 12, B1=250000, B2=25000000)
2^13009+1 has a factor: 3412996903133086890043 (ECM curve 5, B1=250000, B2=25000000)
2^13009+1 has a factor: 5480610406536181849 (ECM curve 1, B1=250000, B2=25000000)
2^13033+1 has a factor: 143013908225680787 (ECM curve 1, B1=250000, B2=25000000)
2^13049+1 has a factor: 2955952215450604470910298923341547 (ECM curve 267, B1=250000, B2=25000000)
2^13063+1 has a factor: 14014340215817143739917841 (ECM curve 49, B1=250000, B2=25000000)
2^13063+1 has a factor: 68013077327374642357457 (ECM curve 3, B1=250000, B2=25000000)
2^13099+1 has a factor: 9242594371158618761018219 (ECM curve 244, B1=250000, B2=25000000)
2^13127+1 has a factor: 17214435134378762972539923739 (ECM curve 144, B1=250000, B2=25000000)
2^13159+1 has a factor: 813675034649817708033689 (ECM curve 31, B1=250000, B2=25000000)
2^13187+1 has a factor: 1347982088004953190910293690453105371 (ECM curve 34, B1=250000, B2=25000000)
2^13187+1 has a factor: 454097554288369742627 (ECM curve 7, B1=250000, B2=25000000)
2^13187+1 has a factor: 745586015811971491427 (ECM curve 21, B1=250000, B2=25000000)
2^13187+1 has a factor: 7934490443941536547 (ECM curve 4, B1=250000, B2=25000000)
2^13217+1 has a factor: 8771795783552843834449 (ECM curve 1, B1=250000, B2=25000000)
2^13241+1 has a factor: 19215441829754883815587946203 (ECM curve 272, B1=250000, B2=25000000)
2^13259+1 has a factor: 107594639606037999264107 (ECM curve 61, B1=250000, B2=25000000)
2^13297+1 has a factor: 20931114094738149331 (ECM curve 14, B1=250000, B2=25000000)
2^13313+1 has a factor: 14463829018588707706361587 (ECM curve 159, B1=250000, B2=25000000)
2^13313+1 has a factor: 321161194126881272243 (ECM curve 20, B1=250000, B2=25000000)
2^13397+1 has a factor: 20550098368339317593 (ECM curve 14, B1=250000, B2=25000000)
2^13487+1 has a factor: 12170354509085241659 (ECM curve 6, B1=250000, B2=25000000)
[/CODE]

axn 2018-09-09 07:31

13500-14000
[CODE]2^13513+1 has a factor: 8808262992911546624792617 (ECM curve 4, B1=250000, B2=25000000)
2^13591+1 has a factor: 68903179044844512863801 (ECM curve 122, B1=250000, B2=25000000)
2^13591+1 has a factor: 92056887579913293831571321 (ECM curve 17, B1=250000, B2=25000000)
2^13597+1 has a factor: 23417146951094800061371 (ECM curve 10, B1=250000, B2=25000000)
2^13649+1 has a factor: 29856050340803541213889 (ECM curve 8, B1=250000, B2=25000000)
2^13649+1 has a factor: 486262504141769197711003 (ECM curve 35, B1=250000, B2=25000000)
2^13679+1 has a factor: 2378518367643070744457 (ECM curve 3, B1=250000, B2=25000000)
2^13721+1 has a factor: 2511224597938984787 (ECM curve 3, B1=250000, B2=25000000)
2^13757+1 has a factor: 315679000498775417369019306283 (ECM curve 95, B1=250000, B2=25000000)
2^13759+1 has a factor: 1978261087330200095450393 (ECM curve 60, B1=250000, B2=25000000)
2^13831+1 has a factor: 10228328487356961484564051 (ECM curve 196, B1=250000, B2=25000000)
2^13859+1 has a factor: 4688997444081272296283 (ECM curve 18, B1=250000, B2=25000000)
2^13873+1 has a factor: 4623892105094780077484139184043 (ECM curve 229, B1=250000, B2=25000000)
2^13873+1 has a factor: 4830048297791089822737940354987 (ECM curve 44, B1=250000, B2=25000000)
2^13879+1 has a factor: 221783315311229318377 (ECM curve 50, B1=250000, B2=25000000)
2^13903+1 has a factor: 913771450717194279748891 (ECM curve 64, B1=250000, B2=25000000)
2^13907+1 has a factor: 12715859216463685074922978187 (ECM curve 2, B1=250000, B2=25000000)
2^13999+1 has a factor: 15783964426811771409217046077969 (ECM curve 372, B1=250000, B2=25000000)
2^13999+1 has a factor: 28670704658751748955377 (ECM curve 18, B1=250000, B2=25000000)
[/CODE]

pinhodecarlos 2018-09-09 10:48

Hi A. Nair,


I would like to help you out, what should I do? Are you running it on Prime95, if so how do I set it up for ecm on 4 threads?


TIA.



Carlos

axn 2018-09-09 15:42

4 Attachment(s)
[QUOTE=pinhodecarlos;495738] I would like to help you out, what should I do? Are you running it on Prime95, if so how do I set it up for ecm on 4 threads?[/QUOTE]

Thanks Carlos. I'm using Prime95 for this. Since this is Wagstaff numbers, we don't use primenet for this work, so everything has to be done manually. If you're familiar with operating P95 in non-GIMPS mode, you can just pick the WUs from the attachments, add it to worktodo.txt and be on your way. If you're starting from scratch, here are the steps (assuming Windows).

1) Copy P95 executable to a folder (preferably NOT under program files). Run it. If it is the first time, it will ask for "using GIMPS" or "Just stress testing", pick the stress testing option. After that, exit prime95.

2) Edit local.txt, and add/modify the following options:
[CODE]WorkerThreads=4
ThreadsPerTest=1
Memory=1000 during 7:30-23:30 else 1000
[/CODE]

3) Edit prime.txt, and add/modify
[CODE]OutputIterations=5000000
ContinueECM=1[/CODE]

4) Edit (or create) worktodo.txt, and add the following 4 sections:
[CODE][Worker #1]

[Worker #2]

[Worker #3]

[Worker #4][/CODE]
In each section, add some work items.

You can pick WUs from the attachments. If you have a modern quad core (Haswell or later) running 24x7, I'd suggest to select all 4 files, because it would be done in a day or two.

Once done, post the results.txt here, and optionally, report the factors to Factordb. If you need a new batch of work, let me know and I'll post it here.

pinhodecarlos 2018-09-09 17:01

Thank you Nair. Running on two threads to minimise the heat generation since this is a laptop.

pinhodecarlos 2018-09-09 20:22

[QUOTE=pinhodecarlos;495766]Thank you Nair. Running on two threads to minimise the heat generation since this is a laptop.[/QUOTE]

BTW, not sure if I was clear but I’m running from 14500 to 16500 on two threads.

axn 2018-09-10 04:06

[QUOTE=pinhodecarlos;495774]BTW, not sure if I was clear but I’m running from 14500 to 16500 on two threads.[/QUOTE]

Acknowledged.

axn 2018-09-10 16:46

[QUOTE=GP2;494952]15313
20201
21613
[/QUOTE]
These three are now proven.

pinhodecarlos 2018-09-13 20:30

1 Attachment(s)
Backup of my range 14500 to 16500 done so far.

axn 2018-09-14 03:22

[QUOTE=pinhodecarlos;496030]Backup of my range 14500 to 16500 done so far.[/QUOTE]

Cool! 37 factors so far. Keep'em coming!

axn 2018-09-14 05:10

14000-14500
[CODE]2^14057+1 has a factor: 303617278353531220291 (ECM curve 13, B1=250000, B2=25000000)
2^14071+1 has a factor: 6284915201425184033 (ECM curve 8, B1=250000, B2=25000000)
2^14083+1 has a factor: 1603417225189416457 (ECM curve 7, B1=250000, B2=25000000)
2^14149+1 has a factor: 53418048453306496403958415165057 (ECM curve 519, B1=250000, B2=25000000)
2^14153+1 has a factor: 47682915920012284739 (ECM curve 7, B1=250000, B2=25000000)
2^14197+1 has a factor: 2417167347336037885557782355257 (ECM curve 118, B1=250000, B2=25000000)
2^14207+1 has a factor: 294983973749096603 (ECM curve 1, B1=250000, B2=25000000)
2^14281+1 has a factor: 37521237292473011219 (ECM curve 19, B1=250000, B2=25000000)
2^14321+1 has a factor: 73769434029495330490187 (ECM curve 115, B1=250000, B2=25000000)
2^14323+1 has a factor: 1559762298208221751399939 (ECM curve 10, B1=250000, B2=25000000)
2^14347+1 has a factor: 7324512501388886539 (ECM curve 10, B1=250000, B2=25000000)
2^14449+1 has a factor: 355297215381766526377057 (ECM curve 30, B1=250000, B2=25000000)
2^14461+1 has a factor: 5833929203942578521737 (ECM curve 7, B1=250000, B2=25000000)
[/CODE]

Continuing with 16500-17000

MisterBitcoin 2018-09-14 06:07

Do you have a list with PRP´s / cofactor PRP´s that need a prove?

GP2 2018-09-14 07:21

[QUOTE=MisterBitcoin;496049]Do you have a list with PRP´s / cofactor PRP´s that need a prove?[/QUOTE]

[URL="http://factordb.com/index.php?id=1100000000026866864"]32369[/URL]
[URL="http://factordb.com/index.php?id=1100000000591997208"]41269[/URL]
and the others are above 80k

axn 2018-09-15 18:40

(2^16729+1)/3 = 301123 · 57365915771 · 96650433856277903079913 · 27900051005133099320370700483 · P4968

PRIMO certificate is available in factordb.

pinhodecarlos 2018-09-15 18:54

Think within 5-6 days I’ll need another batch of files but I was wondering three things:
1) clear prime95 running two threads generates almost the same heat as 4 instances of ecmclient. Maybe I’ll run ecm instead.
2) if running standalone ecm I’ll need to use excel to format the composite but I can’t remember how to run batch jobs.
3) if using prime95 I can remember what worktodo extension file should I use to add more work to the current batch folder.

TIA.

GP2 2018-09-15 19:59

[QUOTE=pinhodecarlos;496140]
3) if using prime95 I can remember what worktodo extension file should I use to add more work to the current batch folder.
[/QUOTE]

[c]worktodo.add[/c] or [c]worktodo.add.txt[/c]

Both of these work on either Windows or Linux.

pinhodecarlos 2018-09-15 21:34

[QUOTE=GP2;496143][c]worktodo.add[/c] or [c]worktodo.add.txt[/c]

Both of these work on either Windows or Linux.[/QUOTE]

Thank you GP2. Wasn’t GP3 the best formula one PC game from micropose?!
Anyway, I’m done with [14500,15000] and [15500,16000] and the other ranges are still underway.

axn 2018-09-17 10:22

16500-17000
[CODE]2^16553+1 has a factor: 24255740240695470491 (ECM curve 1, B1=250000, B2=25000000)
2^16553+1 has a factor: 7154053018754849945563697 (ECM curve 97, B1=250000, B2=25000000)
2^16573+1 has a factor: 696649544614857521 (ECM curve 1, B1=250000, B2=25000000)
2^16603+1 has a factor: 15585137074585080458129252635718353 (ECM curve 101, B1=250000, B2=25000000)
2^16607+1 has a factor: 303320328422719887497 (ECM curve 35, B1=250000, B2=25000000)
2^16619+1 has a factor: 1151577374018700125678948761 (ECM curve 72, B1=250000, B2=25000000)
2^16649+1 has a factor: 14738684332216197916018591568291 (ECM curve 328, B1=250000, B2=25000000)
2^16657+1 has a factor: 789629909044670355787468891 (ECM curve 154, B1=250000, B2=25000000)
2^16729+1 has a factor: 27900051005133099320370700483 (ECM curve 279, B1=250000, B2=25000000)
2^16729+1 has a factor: 96650433856277903079913 (ECM curve 12, B1=250000, B2=25000000)
2^16741+1 has a factor: 809804835360656414883168237139 (ECM curve 243, B1=250000, B2=25000000)
2^16763+1 has a factor: 20134727690344808240068001 (ECM curve 136, B1=250000, B2=25000000)
2^16823+1 has a factor: 1679052693166082395351642577 (ECM curve 38, B1=250000, B2=25000000)
2^16829+1 has a factor: 501981017684293624882492979 (ECM curve 66, B1=250000, B2=25000000)
2^16829+1 has a factor: 7030862200846423842337531 (ECM curve 6, B1=250000, B2=25000000)
2^16831+1 has a factor: 52888863505346416714097 (ECM curve 16, B1=250000, B2=25000000)
2^16831+1 has a factor: 6337591265234038183048243 (ECM curve 98, B1=250000, B2=25000000)
2^16871+1 has a factor: 6454068146099797732673515409 (ECM curve 113, B1=250000, B2=25000000)
2^16903+1 has a factor: 640701004988163401 (ECM curve 3, B1=250000, B2=25000000)
[/CODE]

pinhodecarlos 2018-09-21 13:22

1 Attachment(s)
My range is done.


14500-16500

axn 2018-09-24 02:29

17000-17500
[CODE]2^17021+1 has a factor: 19970118882517760713844757569 (ECM curve 270, B1=250000, B2=25000000)
2^17041+1 has a factor: 46936866960519129408225318409 (ECM curve 130, B1=250000, B2=25000000)
2^17077+1 has a factor: 3553221273890775977131483 (ECM curve 14, B1=250000, B2=25000000)
2^17093+1 has a factor: 6434901203451482177147 (ECM curve 15, B1=250000, B2=25000000)
2^17137+1 has a factor: 74065101935672709731614369 (ECM curve 170, B1=250000, B2=25000000)
2^17159+1 has a factor: 180366271112782247999249803 (ECM curve 9, B1=250000, B2=25000000)
2^17167+1 has a factor: 7199673061767521949212888347 (ECM curve 91, B1=250000, B2=25000000)
2^17239+1 has a factor: 15743980144824856474553 (ECM curve 16, B1=250000, B2=25000000)
2^17239+1 has a factor: 9265020153871021580804299 (ECM curve 125, B1=250000, B2=25000000)
2^17291+1 has a factor: 127151453638503039336813703937 (ECM curve 135, B1=250000, B2=25000000)
2^17291+1 has a factor: 5494662222282781553959883 (ECM curve 44, B1=250000, B2=25000000)
2^17327+1 has a factor: 279194784644349188143579 (ECM curve 44, B1=250000, B2=25000000)
2^17359+1 has a factor: 189729835257594067 (ECM curve 2, B1=250000, B2=25000000)
2^17377+1 has a factor: 1598815760606505821467 (ECM curve 32, B1=250000, B2=25000000)
2^17393+1 has a factor: 310471675824874318553 (ECM curve 1, B1=250000, B2=25000000)
2^17393+1 has a factor: 97019705507132797228107411041 (ECM curve 47, B1=250000, B2=25000000)
2^17401+1 has a factor: 284292996618239242781965355931769 (ECM curve 284, B1=250000, B2=25000000)
2^17419+1 has a factor: 478541207978011275399739 (ECM curve 71, B1=250000, B2=25000000)
2^17477+1 has a factor: 959936791635270283 (ECM curve 1, B1=250000, B2=25000000)
2^17491+1 has a factor: 1127373789196363561966486313683 (ECM curve 67, B1=250000, B2=25000000)
2^17551+1 has a factor: 25735713653693529449 (ECM curve 8, B1=250000, B2=25000000)
[/CODE]

axn 2018-09-24 02:30

[QUOTE=pinhodecarlos;496520]My range is done.


14500-16500[/QUOTE]

Hmmm... Somehow I missed this message. Do you need another set of tests?

pinhodecarlos 2018-09-24 08:06

[QUOTE=axn;496649]Hmmm... Somehow I missed this message. Do you need another set of tests?[/QUOTE]

Yes please, same range size.

axn 2018-09-24 08:46

1 Attachment(s)
[QUOTE=pinhodecarlos;496664]Yes please, same range size.[/QUOTE]

Ok, here is the 18000-20000 range.

BTW, did you check the relative performance of P95 vs GMP-ECM on these numbers? In my trials, P95 was way faster so that two core P95 was more throughput than 4 core GMP-ECM.

pinhodecarlos 2018-09-24 09:40

[QUOTE=axn;496666]Ok, here is the 18000-20000 range.

BTW, did you check the relative performance of P95 vs GMP-ECM on these numbers? In my trials, P95 was way faster so that two core P95 was more throughput than 4 core GMP-ECM.[/QUOTE]

Thank you. Did the trial yesterday and matches your results so I’ll run Prime95.

GP2 2018-09-25 13:31

It appears that the set of all factors of all Mersenne numbers with prime exponent and the set of all factors of all Wagstaff numbers with prime exponent are disjoint. Is there an elementary proof of this?

By contrast, for other pairs of b values in (b[sup]p[/sup] − 1) / (b − 1), there are many factors in common: for b = 2 and 3, 2 and 5, 3 and 5; −2 and 3, −2 and 5... but not 2 and −2.

For example: (3[SUP]5[/SUP] − 1) /2 = [B]11[/B][SUP]2[/SUP] and (5[SUP]5[/SUP] − 1) /4 = [B]11[/B] × 71

Incidentally, that's the only non-squarefree factor of a repunit that I know of. Sure would be nice if we could find one for Mersennes... I keep checking.

For a random pair of repunit bases b[SUB]1[/SUB], b[SUB]2[/SUB] such that b[SUB]1[/SUB] ≠ −b[SUB]2[/SUB], would the set of common factors be finite or infinite?

paulunderwood 2018-09-25 13:35

[QUOTE=GP2;496734]It appears that the set of all factors of all Mersenne numbers with prime exponent and the set of all factors of all Wagstaff numbers with prime exponent are disjoint. Is there an elementary proof of this?
[/QUOTE]

Factors of Mersennes are 8*n+-1 and factors of Wagstaff are 8*m+-3.

R. Gerbicz 2018-09-25 13:46

[QUOTE=GP2;496734]It appears that the set of all factors of all Mersenne numbers with prime exponent and the set of all factors of all Wagstaff numbers with prime exponent are disjoint. Is there an elementary proof of this?
[/QUOTE]

There is a single exception: 2^2-1 and (2^3+1)/3 are divisible by 3. (and actually they are equal to 3). And there is no more solution:

Assume that 1<d | 2^p-1 and (2^q+1)/3, where p,q are odd primes.
Then obviously p!=q, otherwise d | 2^p-1 and 2^p+1, so d | 2, what is impossible.
We can write:
d | gcd(2^p-1,2^q+1) | gcd(2^p-1,2^(2*q)-1)=2^gcd(p,2*q)-1=2^1-1=1

where used: gcd(p,2*q)=1, because p is odd and p!=q primes.

axn 2018-09-26 02:39

[QUOTE=paulunderwood;496736]Factors of Mersennes are 8*n+-1 and factors of Wagstaff are 8*m+-3.[/QUOTE]
That is incorrect. Wagstaff factors are 8n + {1,3}. So 1 (mod 8) is a common class for both of them.

[QUOTE=GP2;496734]It appears that the set of all factors of all Mersenne numbers with prime exponent and the set of all factors of all Wagstaff numbers with prime exponent are disjoint. Is there an elementary proof of this?
[/QUOTE]
Yes, znorder( Mod(2, f) ) = p for f | 2^p-1 and znorder( Mod(2, g) ) = 2p where g | (2^p+1)/3. Therefore they are disjoint sets.

paulunderwood 2018-09-26 02:48

[QUOTE=axn;496778]That is incorrect. Wagstaff factors are 8n + {1,3}. So 1 (mod 8) is a common class for both of them.
[/QUOTE]

Thanks for the correction! :blush:

R. Gerbicz 2018-09-26 07:41

[QUOTE=axn;496778]
Yes, znorder( Mod(2, f) ) = p for f | 2^p-1 and znorder( Mod(2, g) ) = 2p where g | (2^p+1)/3. Therefore they are disjoint sets.[/QUOTE]

Wrong proof. Nobody (except me) recognise that p=3 is a common factor?

axn 2018-09-26 11:38

[QUOTE=R. Gerbicz;496792]Wrong proof. Nobody (except me) recognise that p=3 is a common factor?[/QUOTE]

Except for the trivial exception of 3, are there any other case where the proof fails?

pinhodecarlos 2018-09-29 15:12

2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime!


[URL="http://factordb.com/index.php?query=2%5E19379%2B1"]http://factordb.com/index.php?query=2%5E19379%2B1[/URL]


P5804 [URL]http://factordb.com/index.php?id=1100000001172464482[/URL]

paulunderwood 2018-09-29 15:25

[QUOTE=pinhodecarlos;497063]2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime!


[URL="http://factordb.com/index.php?query=2%5E19379%2B1"]http://factordb.com/index.php?query=2%5E19379%2B1[/URL]


P5804 [URL]http://factordb.com/index.php?id=1100000001172464482[/URL][/QUOTE]

This had me fooled at first, but:

[CODE]factor 1767177497789872389034125489321
1767177497789872389034125489321: 3 11627401 50661292745468868151307
[/CODE]

and:
[CODE]
time ./pfgw64 -k -f0 -od -q"(2^19379+1)/3/50661292745468868151307/11627401" | ../../coding/gwnum/s2 - 1 2 19379 1

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

real 0m0.212s
user 0m0.304s
sys 0m0.000s
[/CODE]

axn 2018-09-29 16:04

[QUOTE=pinhodecarlos;497063]2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime![/QUOTE]

:w00t: Congratulations!

axn 2018-09-30 07:54

17500-18000
[CODE]2^17551+1 has a factor: 25735713653693529449 (ECM curve 8, B1=250000, B2=25000000)
2^17569+1 has a factor: 179227535070013504018942273739 (ECM curve 98, B1=250000, B2=25000000)
2^17569+1 has a factor: 2206370228865414510833059 (ECM curve 7, B1=250000, B2=25000000)
2^17581+1 has a factor: 105547448860925250997366606819 (ECM curve 483, B1=250000, B2=25000000)
2^17581+1 has a factor: 40091191606504248827275161779123 (ECM curve 98, B1=250000, B2=25000000)
2^17623+1 has a factor: 698517626064061766822912882747 (ECM curve 25, B1=250000, B2=25000000)
2^17627+1 has a factor: 19897288830906370321 (ECM curve 44, B1=250000, B2=25000000)
2^17681+1 has a factor: 1640778478824054691934851 (ECM curve 139, B1=250000, B2=25000000)
2^17707+1 has a factor: 145380863162377258174769 (ECM curve 64, B1=250000, B2=25000000)
2^17713+1 has a factor: 621845319559233013940510249 (ECM curve 196, B1=250000, B2=25000000)
2^17737+1 has a factor: 1176542531701657484481082913 (ECM curve 212, B1=250000, B2=25000000)
2^17783+1 has a factor: 12488572654928988532921782764588801 (ECM curve 298, B1=250000, B2=25000000)
2^17807+1 has a factor: 553279164410641071695422843 (ECM curve 151, B1=250000, B2=25000000)
2^17807+1 has a factor: 63431661672479249 (ECM curve 1, B1=250000, B2=25000000)
2^17827+1 has a factor: 6486130363802766148587218449 (ECM curve 357, B1=250000, B2=25000000)
2^17851+1 has a factor: 8989993295392804145476248169 (ECM curve 225, B1=250000, B2=25000000)
2^17863+1 has a factor: 74167942985744072715878249 (ECM curve 11, B1=250000, B2=25000000)
2^17881+1 has a factor: 2806154593843559467 (ECM curve 10, B1=250000, B2=25000000)
2^17957+1 has a factor: 40852609716914003537511405329 (ECM curve 348, B1=250000, B2=25000000)
2^17959+1 has a factor: 461118648758359233113203 (ECM curve 31, B1=250000, B2=25000000)[/CODE]

axn 2018-09-30 17:00

20000-22000
[CODE]2^20023+1 has a factor: 37510552791647458771
2^20051+1 has a factor: 257425412435536649
2^20051+1 has a factor: 3869488172299271890904297
2^20063+1 has a factor: 4659288072900311334648711315841
2^20107+1 has a factor: 2743589598602187505747
2^20117+1 has a factor: 4890446030623424048707
2^20129+1 has a factor: 46208108810799404871122419
2^20143+1 has a factor: 964033675819142651
2^20161+1 has a factor: 134469591069683
2^20173+1 has a factor: 743601397045097627453299
2^20219+1 has a factor: 182985666224987960298637765803059
2^20233+1 has a factor: 4189494144638412163
2^20249+1 has a factor: 6271693669868573161299252319777
2^20261+1 has a factor: 3103962310297339
2^20297+1 has a factor: 13133704985817620272140420384689
2^20333+1 has a factor: 47794427621302424593025083
2^20359+1 has a factor: 857182102209462004718363615779
2^20389+1 has a factor: 4106216082433866721
2^20407+1 has a factor: 1991711889529714740363107681
2^20477+1 has a factor: 4408421234877896603
2^20479+1 has a factor: 2403526884029539686014236094659
2^20479+1 has a factor: 3422976667427
2^20483+1 has a factor: 11413480849819
2^20483+1 has a factor: 1924821469502924137
2^20521+1 has a factor: 3109639586095160002494173679115321
2^20533+1 has a factor: 20557323121358214361
2^20543+1 has a factor: 2308491964735217383129886833
2^20563+1 has a factor: 2522018807708129
2^20593+1 has a factor: 8157158140843971595528897248457
2^20611+1 has a factor: 4167333623203120606265560076873
2^20627+1 has a factor: 16001463124310535561113
2^20641+1 has a factor: 1680552399763578899
2^20641+1 has a factor: 44709189903899
2^20693+1 has a factor: 11039167817257937443157587
2^20693+1 has a factor: 32372699951864750067423360211
2^20719+1 has a factor: 283203828833237869481
2^20749+1 has a factor: 20391614891030525371
2^20753+1 has a factor: 48003675801500392248161
2^20789+1 has a factor: 1364080160622986883250321266667
2^20789+1 has a factor: 214237277547136797379
2^20807+1 has a factor: 5750818063280593
2^20849+1 has a factor: 156575928020521902700628923
2^20849+1 has a factor: 711635844333463783790443043
2^20857+1 has a factor: 71042575998539
2^20873+1 has a factor: 532684992928685427252905009
2^20903+1 has a factor: 18661968104583443235718665731
2^20921+1 has a factor: 2027720050341472185904615803073
2^20921+1 has a factor: 335520589852300390243
2^20939+1 has a factor: 20933804099550553
2^20947+1 has a factor: 3088382574101887558709344614683
2^20963+1 has a factor: 4355362012024784470653011
2^20981+1 has a factor: 51942572296376948317505038164957371
2^21013+1 has a factor: 3668929788863717138772900457
2^21017+1 has a factor: 16593735922243244859134070491
2^21023+1 has a factor: 2660003581454497729459
2^21031+1 has a factor: 15498026210331776641
2^21059+1 has a factor: 10892326048051503533266007123
2^21067+1 has a factor: 19933173060194242778264017
2^21101+1 has a factor: 20275268810217203
2^21121+1 has a factor: 150766158290940179027587
2^21121+1 has a factor: 764232573191224161100819
2^21121+1 has a factor: 86463076942819
2^21149+1 has a factor: 3230258365665452655137
2^21163+1 has a factor: 95559678958037312400273961
2^21211+1 has a factor: 3832944410199417231337
2^21211+1 has a factor: 683495906696251150826234104545947
2^21247+1 has a factor: 48095430631346489
2^21313+1 has a factor: 568787927050811249
2^21317+1 has a factor: 11298468738572894718067
2^21317+1 has a factor: 4389851798588466214795562339
2^21341+1 has a factor: 449867031167363
2^21341+1 has a factor: 49591774383454134099132643
2^21379+1 has a factor: 1299003843005694933567331
2^21379+1 has a factor: 54798678469523996671365241
2^21383+1 has a factor: 3438568416814276987709579
2^21391+1 has a factor: 134477468200008576403553689313
2^21391+1 has a factor: 43007001846266587
2^21397+1 has a factor: 167380355069488915217
2^21467+1 has a factor: 806646395384184216569
2^21487+1 has a factor: 5758749036874074697366069067
2^21493+1 has a factor: 25553144664907
2^21503+1 has a factor: 16916741153700802937
2^21523+1 has a factor: 77381746151979035203
2^21529+1 has a factor: 1702941136495035897886291
2^21529+1 has a factor: 465086981569239321244339
2^21557+1 has a factor: 4694330692397593661473
2^21569+1 has a factor: 361772772464521091
2^21569+1 has a factor: 425895424990514993
2^21587+1 has a factor: 579269658222000497
2^21649+1 has a factor: 1413110454707564001068513
2^21649+1 has a factor: 50269535917652870459
2^21649+1 has a factor: 6922502237649947040849362251
2^21661+1 has a factor: 475888569773731407813690353
2^21727+1 has a factor: 49809185155493429630858507
2^21737+1 has a factor: 177903299744917729
2^21751+1 has a factor: 542538499273227893441
2^21757+1 has a factor: 22624105778237266001406089
2^21773+1 has a factor: 2487149567869465481
2^21773+1 has a factor: 308672408980908803
2^21787+1 has a factor: 50290917986637486315257
2^21803+1 has a factor: 144985052235826097
2^21821+1 has a factor: 30696428098561013756621570419963
2^21863+1 has a factor: 13204242361797596073473843
2^21881+1 has a factor: 156579746660319571
2^21881+1 has a factor: 24286354927538843123
2^21893+1 has a factor: 1031342237529259
2^21893+1 has a factor: 23100546344437470254058168365009
2^21893+1 has a factor: 34722125531238472939
2^21911+1 has a factor: 23235161223671815545480155441
2^21961+1 has a factor: 765091067506747755283
2^21977+1 has a factor: 9552297931135241269073[/CODE]

pinhodecarlos 2018-10-05 11:04

Almost done with 18000-20000.

axn 2018-10-05 11:14

[QUOTE=pinhodecarlos;497404]Almost done with 18000-20000.[/QUOTE]

Sure. I'll send you the next range (24500-26500) shortly. Let me know if you want to adjust the range up/down.

pinhodecarlos 2018-10-05 11:55

[QUOTE=axn;497406]Sure. I'll send you the next range (24500-26500) shortly. Let me know if you want to adjust the range up/down.[/QUOTE]

I’m ok with it, thank you.

axn 2018-10-05 14:03

[QUOTE=pinhodecarlos;497408]I’m ok with it, thank you.[/QUOTE]

YGM

pinhodecarlos 2018-10-05 14:26

Thank you.
Will be processing 24500-26500.

axn 2018-10-06 07:48

22500-24500
[CODE]2^22501+1 has a factor: 363852407988272192923
2^22511+1 has a factor: 1033304721851687430514547
2^22541+1 has a factor: 1416177937792460923
2^22541+1 has a factor: 2543898210018238270707588473
2^22543+1 has a factor: 77553926444351131889
2^22571+1 has a factor: 16224211292755655050486966169
2^22573+1 has a factor: 4833320507779089843909063667
2^22613+1 has a factor: 17891128189926660451
2^22619+1 has a factor: 20446827137786706393252811
2^22637+1 has a factor: 17711589057584298304177
2^22637+1 has a factor: 46641027047506205260753
2^22639+1 has a factor: 35256743343228048742183504987
2^22643+1 has a factor: 1412890053119709881
2^22651+1 has a factor: 61991110485211530656857
2^22669+1 has a factor: 4323016614982902606570384066913
2^22669+1 has a factor: 615459478525037586049
2^22679+1 has a factor: 280132422758112417542587
2^22691+1 has a factor: 2897677731973376857507
2^22709+1 has a factor: 14655473989013855567796274907
2^22787+1 has a factor: 42735085298654378046761
2^22807+1 has a factor: 12704388993839326918969
2^22807+1 has a factor: 756480335806324322819
2^22811+1 has a factor: 9221232670315620775164203
2^22861+1 has a factor: 119682099831736311320319811
2^22871+1 has a factor: 660100946988445331459939
2^22877+1 has a factor: 743950809492185371
2^22901+1 has a factor: 408738005480076438707
2^22907+1 has a factor: 112658057238296369004783377
2^22937+1 has a factor: 14706466947259847948161814923
2^22943+1 has a factor: 6978883295162826928136401
2^22963+1 has a factor: 998783444523492005013833
2^22993+1 has a factor: 62412836486995292557385801
2^23017+1 has a factor: 1394108515980717020663793907
2^23027+1 has a factor: 1381965840865372097
2^23041+1 has a factor: 21107647000470539819
2^23041+1 has a factor: 3382713944601186289
2^23053+1 has a factor: 1588979086144103462297
2^23057+1 has a factor: 24401017933475426209989161
2^23081+1 has a factor: 7312499405279940466733460227
2^23087+1 has a factor: 118732486456937746409
2^23117+1 has a factor: 94550802675553265754073139
2^23131+1 has a factor: 184032938654518258078250753
2^23159+1 has a factor: 233320219277705865702547
2^23159+1 has a factor: 3903414027531892291000129489
2^23197+1 has a factor: 1250738342261755182180386783737
2^23201+1 has a factor: 72933212973106609337996945793979
2^23201+1 has a factor: 7541646033665262289149120992417
2^23227+1 has a factor: 18744017516505605060705751641
2^23227+1 has a factor: 8614967343686291353600987
2^23269+1 has a factor: 55581327422797074523
2^23291+1 has a factor: 61453477595186414151204691883
2^23291+1 has a factor: 8323919389547
2^23297+1 has a factor: 1242425663182474003
2^23297+1 has a factor: 25107183663338195611433
2^23333+1 has a factor: 10008188612516856078372320801
2^23333+1 has a factor: 626417189970223423552312395401
2^23339+1 has a factor: 9425733004489657057
2^23357+1 has a factor: 1758028102656875051609764418150947
2^23371+1 has a factor: 17097169446392151749853523
2^23447+1 has a factor: 5885572526457741870508307
2^23509+1 has a factor: 12531247984968118878608011
2^23509+1 has a factor: 9008637750645709609649
2^23531+1 has a factor: 258484871836732184731
2^23539+1 has a factor: 21980268632874981788867
2^23539+1 has a factor: 4010104673247673357345201
2^23563+1 has a factor: 646874171743558951296011
2^23599+1 has a factor: 356028874240546099553
2^23599+1 has a factor: 40752186645926993
2^23599+1 has a factor: 42792293469375604937662574713
2^23599+1 has a factor: 6994038563827681
2^23623+1 has a factor: 743780838757399557019153
2^23627+1 has a factor: 1602414390182461060697
2^23629+1 has a factor: 45612554577153685092371
2^23719+1 has a factor: 22790264861318215297
2^23741+1 has a factor: 402077485579919771838371
2^23741+1 has a factor: 51525528708133475982262729
2^23743+1 has a factor: 150063844270216604747641
2^23743+1 has a factor: 677608512711603124521385721
2^23753+1 has a factor: 795255130535502230271864422219
2^23753+1 has a factor: 96635499773203812931432260307883
2^23767+1 has a factor: 34688867984128061572350491
2^23789+1 has a factor: 7206237207543503697858473
2^23831+1 has a factor: 27768740742227469693427
2^23833+1 has a factor: 1390916989479492549853266355913
2^23833+1 has a factor: 196530492822767044236550735979
2^23833+1 has a factor: 4872249222887975602436396113
2^23857+1 has a factor: 1100950159734959508762542603
2^23869+1 has a factor: 1718286921105770947
2^23869+1 has a factor: 99841960601449912071241
2^23911+1 has a factor: 14542603511007054781589371
2^23917+1 has a factor: 10808115367181027368949865148523
2^23917+1 has a factor: 145455384021321641
2^23971+1 has a factor: 190575280843674341902057
2^23977+1 has a factor: 143342857883960549807275817
2^23977+1 has a factor: 249077941768580631405022993
2^24007+1 has a factor: 13397048427233764742694209
2^24019+1 has a factor: 266412898276229635958085937
2^24023+1 has a factor: 243817461347649714384638203
2^24043+1 has a factor: 2894172037699636594430209
2^24049+1 has a factor: 23331897322989813913
2^24049+1 has a factor: 733023770892999929027
2^24061+1 has a factor: 1487979749092961748451043
2^24113+1 has a factor: 8284988543734251804199217097193
2^24113+1 has a factor: 8289764104312692763
2^24121+1 has a factor: 5137377704003843557417
2^24121+1 has a factor: 8753680476220918679996870171
2^24133+1 has a factor: 6583388199032344582874244203
2^24137+1 has a factor: 219679377592704035975302363
2^24151+1 has a factor: 909744245423996847546001
2^24181+1 has a factor: 229654584107721097422841
2^24203+1 has a factor: 1210981942987106673137
2^24223+1 has a factor: 1378328669128933411
2^24329+1 has a factor: 689775681927334002907
2^24337+1 has a factor: 9604746321964943209571531
2^24371+1 has a factor: 7952841229603135943321
2^24373+1 has a factor: 2328266095022563841038317132993161
2^24379+1 has a factor: 104928190322064926262900409
2^24391+1 has a factor: 2506762236502012707919414776379
2^24413+1 has a factor: 25056488273094515686217
2^24421+1 has a factor: 98051225469241147
[/CODE]

GP2 2018-10-06 17:56

[QUOTE=axn;497145]20000-22000[/QUOTE]

[QUOTE=axn;497484]22500-24500[/QUOTE]

Hmmm, maybe there is a gap from 22000 to 22500?

axn 2018-10-07 02:38

[QUOTE=GP2;497509]Hmmm, maybe there is a gap from 22000 to 22500?[/QUOTE]

Different computer - will finish in a few hours.

axn 2018-10-07 14:23

[QUOTE=axn;497533]Different computer - will finish in a few hours.[/QUOTE]

And here is 22000-22500
[CODE]2^22013+1 has a factor: 161216149365081802666561 (ECM curve 102, B1=250000, B2=25000000)
2^22027+1 has a factor: 3045039965757597246457 (ECM curve 5, B1=250000, B2=25000000)
2^22039+1 has a factor: 3148545348434371354717267 (ECM curve 56, B1=250000, B2=25000000)
2^22067+1 has a factor: 44004643599715052134553836136587 (ECM curve 507, B1=250000, B2=25000000)
2^22073+1 has a factor: 7297824105736302541246187 (ECM curve 64, B1=250000, B2=25000000)
2^22109+1 has a factor: 1104914660471587635291575641 (ECM curve 65, B1=250000, B2=25000000)
2^22133+1 has a factor: 2925569040926110441 (ECM curve 17, B1=250000, B2=25000000)
2^22153+1 has a factor: 39044690892848270129 (ECM curve 78, B1=250000, B2=25000000)
2^22157+1 has a factor: 43100835341821191169525750403 (ECM curve 409, B1=250000, B2=25000000)
2^22159+1 has a factor: 429357717967259 (ECM curve 2, B1=250000, B2=25000000)
2^22189+1 has a factor: 6452495674107881 (ECM curve 3, B1=250000, B2=25000000)
2^22193+1 has a factor: 182640027089949999491 (ECM curve 6, B1=250000, B2=25000000)
2^22259+1 has a factor: 345626239590839510349467 (ECM curve 99, B1=250000, B2=25000000)
2^22277+1 has a factor: 1256507458539471863987 (ECM curve 4, B1=250000, B2=25000000)
2^22277+1 has a factor: 46244864019045632180739907 (ECM curve 3, B1=250000, B2=25000000)
2^22279+1 has a factor: 5063888269691607915089455849 (ECM curve 456, B1=250000, B2=25000000)
2^22283+1 has a factor: 150200272993194540713 (ECM curve 11, B1=250000, B2=25000000)
2^22291+1 has a factor: 1132035422307429009133793 (ECM curve 76, B1=250000, B2=25000000)
2^22291+1 has a factor: 1517032886145731 (ECM curve 3, B1=250000, B2=25000000)
2^22307+1 has a factor: 21656470621661870900180979073 (ECM curve 590, B1=250000, B2=25000000)
2^22343+1 has a factor: 236348273432983995411683 (ECM curve 3, B1=250000, B2=25000000)
2^22367+1 has a factor: 248603736785625041 (ECM curve 5, B1=250000, B2=25000000)
2^22391+1 has a factor: 485411004904467283 (ECM curve 3, B1=250000, B2=25000000)
2^22469+1 has a factor: 2812522536993343710283137367147 (ECM curve 404, B1=250000, B2=25000000)
2^22483+1 has a factor: 1376690534283907444603 (ECM curve 17, B1=250000, B2=25000000)
2^22483+1 has a factor: 8458211105044029957420516331 (ECM curve 72, B1=250000, B2=25000000)
[/CODE]

pinhodecarlos 2018-10-08 18:58

18000-19500


[CODE]
2^18013+1 has a factor: 4653908141249917710372183381899 (ECM curve 104, B1=250000, B2=25000000)
2^18041+1 has a factor: 183499772036043411539 (ECM curve 21, B1=250000, B2=25000000)
2^18043+1 has a factor: 2665682071463498638970303809 (ECM curve 321, B1=250000, B2=25000000)
2^18049+1 has a factor: 103846431399903782482127741731 (ECM curve 76, B1=250000, B2=25000000)
2^18059+1 has a factor: 351195381641711171 (ECM curve 4, B1=250000, B2=25000000)
2^18061+1 has a factor: 19414084218681475565980537 (ECM curve 187, B1=250000, B2=25000000)
2^18119+1 has a factor: 1891739341989657624809 (ECM curve 31, B1=250000, B2=25000000)
2^18121+1 has a factor: 2075173865949690806819 (ECM curve 10, B1=250000, B2=25000000)
2^18127+1 has a factor: 3562174572122223433 (ECM curve 1, B1=250000, B2=25000000)
2^18181+1 has a factor: 8762190390745782409 (ECM curve 6, B1=250000, B2=25000000)
2^18199+1 has a factor: 13556288643468872758825073 (ECM curve 51, B1=250000, B2=25000000)
2^18229+1 has a factor: 318105612752089274695606787 (ECM curve 438, B1=250000, B2=25000000)
2^18229+1 has a factor: 38586294522758826029959859 (ECM curve 3, B1=250000, B2=25000000)
2^18289+1 has a factor: 6051506222734635873739 (ECM curve 2, B1=250000, B2=25000000)
2^18307+1 has a factor: 11505593920519021179921539 (ECM curve 88, B1=250000, B2=25000000)
2^18311+1 has a factor: 36278869114491923 (ECM curve 2, B1=250000, B2=25000000)
2^18313+1 has a factor: 533317823771455854465046723 (ECM curve 46, B1=250000, B2=25000000)
2^18379+1 has a factor: 215850830498525998644991891 (ECM curve 92, B1=250000, B2=25000000)
2^18379+1 has a factor: 51982760130131587147 (ECM curve 2, B1=250000, B2=25000000)
2^18397+1 has a factor: 815125252204231208084723 (ECM curve 261, B1=250000, B2=25000000)
2^18397+1 has a factor: 815125252204231208084723 (ECM curve 36, B1=250000, B2=25000000)
2^18401+1 has a factor: 27986308954728312339131 (ECM curve 10, B1=250000, B2=25000000)
2^18427+1 has a factor: 269143881984340030889443186633 (ECM curve 499, B1=250000, B2=25000000)
2^18457+1 has a factor: 31564926226245701093011 (ECM curve 17, B1=250000, B2=25000000)
2^18517+1 has a factor: 29183458945307248681303441 (ECM curve 110, B1=250000, B2=25000000)
2^18517+1 has a factor: 8926185529641283136217479401 (ECM curve 36, B1=250000, B2=25000000)
2^18521+1 has a factor: 305732090421921402941809 (ECM curve 2, B1=250000, B2=25000000)
2^18523+1 has a factor: 7964434608357585343033 (ECM curve 40, B1=250000, B2=25000000)
2^18587+1 has a factor: 22504760608703176471319593393 (ECM curve 11, B1=250000, B2=25000000)
2^18617+1 has a factor: 5706554883342478678633 (ECM curve 9, B1=250000, B2=25000000)
2^18671+1 has a factor: 86607771586475570401 (ECM curve 10, B1=250000, B2=25000000)
2^18701+1 has a factor: 5187827237971354134386620753 (ECM curve 425, B1=250000, B2=25000000)
2^18701+1 has a factor: 568781375709419482563523 (ECM curve 7, B1=250000, B2=25000000)
2^18713+1 has a factor: 21671047549485114830165351867 (ECM curve 221, B1=250000, B2=25000000)
2^18713+1 has a factor: 21671047549485114830165351867 (ECM curve 370, B1=250000, B2=25000000)
2^18743+1 has a factor: 832443768498699377 (ECM curve 10, B1=250000, B2=25000000)
2^18757+1 has a factor: 130117984889129264106615983507 (ECM curve 7, B1=250000, B2=25000000)
2^18793+1 has a factor: 6686340673024886284854023281 (ECM curve 89, B1=250000, B2=25000000)
2^18793+1 has a factor: 8021089772520880399323021907 (ECM curve 366, B1=250000, B2=25000000)
2^18911+1 has a factor: 13753171866552219345645488259833 (ECM curve 205, B1=250000, B2=25000000)
2^18911+1 has a factor: 687378282554763330802093987 (ECM curve 270, B1=250000, B2=25000000)
2^18973+1 has a factor: 262528402968801960327370796218811 (ECM curve 272, B1=250000, B2=25000000)
2^18979+1 has a factor: 305286254265688121147 (ECM curve 33, B1=250000, B2=25000000)
2^19009+1 has a factor: 66099876959391829072457 (ECM curve 12, B1=250000, B2=25000000)
2^19051+1 has a factor: 7171285994154701827 (ECM curve 16, B1=250000, B2=25000000)
2^19051+1 has a factor: 7242790896000701075326109707 (ECM curve 281, B1=250000, B2=25000000)
2^19073+1 has a factor: 3054196594123680587 (ECM curve 7, B1=250000, B2=25000000)
2^19079+1 has a factor: 1350821124572501513 (ECM curve 24, B1=250000, B2=25000000)
2^19087+1 has a factor: 11086063744273130458179394001 (ECM curve 341, B1=250000, B2=25000000)
2^19139+1 has a factor: 21814567186195009 (ECM curve 9, B1=250000, B2=25000000)
2^19141+1 has a factor: 7212376217259423787 (ECM curve 9, B1=250000, B2=25000000)
2^19157+1 has a factor: 2272009822087092028937 (ECM curve 2, B1=250000, B2=25000000)
2^19207+1 has a factor: 132344364209300600047331 (ECM curve 18, B1=250000, B2=25000000)
2^19237+1 has a factor: 4123338625679495946587232961 (ECM curve 129, B1=250000, B2=25000000)
2^19333+1 has a factor: 32457557905667601775174409140361 (ECM curve 169, B1=250000, B2=25000000)
2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
2^19387+1 has a factor: 868623210009257588779 (ECM curve 1, B1=250000, B2=25000000)
2^19421+1 has a factor: 473989358723441305529705975377 (ECM curve 432, B1=250000, B2=25000000)
2^19427+1 has a factor: 6351122650200457612188392757209 (ECM curve 506, B1=250000, B2=25000000)
2^19429+1 has a factor: 8759643661306472758367298763 (ECM curve 136, B1=250000, B2=25000000)
2^19433+1 has a factor: 10556065410084428441 (ECM curve 17, B1=250000, B2=25000000)
2^19447+1 has a factor: 39157333895664987580304724769 (ECM curve 48, B1=250000, B2=25000000)
2^19457+1 has a factor: 1695309104230212938188921 (ECM curve 12, B1=250000, B2=25000000)
2^19463+1 has a factor: 3285277166185155963022241 (ECM curve 85, B1=250000, B2=25000000)
2^19463+1 has a factor: 9277424233772432603 (ECM curve 2, B1=250000, B2=25000000)
2^19469+1 has a factor: 1557748616749332649 (ECM curve 3, B1=250000, B2=25000000)
2^19471+1 has a factor: 2690202511452341470240261937 (ECM curve 65, B1=250000, B2=25000000)
2^19477+1 has a factor: 12556948601334245221407443 (ECM curve 5, B1=250000, B2=25000000)
2^19489+1 has a factor: 20460631918008238217 (ECM curve 27, B1=250000, B2=25000000)

[/CODE]

pinhodecarlos 2018-10-10 17:55

19500-20000


[CODE]
2^19507+1 has a factor: 1234449887923479271291136873 (ECM curve 148, B1=250000, B2=25000000)
2^19507+1 has a factor: 844428452139314289368892697 (ECM curve 24, B1=250000, B2=25000000)
2^19531+1 has a factor: 5454141264689131537 (ECM curve 4, B1=250000, B2=25000000)
2^19543+1 has a factor: 6399980160968211993323 (ECM curve 40, B1=250000, B2=25000000)
2^19559+1 has a factor: 13808866171980325224872459 (ECM curve 26, B1=250000, B2=25000000)
2^19559+1 has a factor: 23194744871436344179 (ECM curve 16, B1=250000, B2=25000000)
2^19571+1 has a factor: 157749577761062936504950403 (ECM curve 65, B1=250000, B2=25000000)
2^19583+1 has a factor: 439845236282857057388505923 (ECM curve 112, B1=250000, B2=25000000)
2^19597+1 has a factor: 48424768917631954134642499 (ECM curve 42, B1=250000, B2=25000000)
2^19597+1 has a factor: 5037260730896363 (ECM curve 1, B1=250000, B2=25000000)
2^19681+1 has a factor: 263718844984195038952184137 (ECM curve 422, B1=250000, B2=25000000)
2^19687+1 has a factor: 213065359260724742393 (ECM curve 5, B1=250000, B2=25000000)
2^19687+1 has a factor: 5427330059655401317187 (ECM curve 90, B1=250000, B2=25000000)
2^19697+1 has a factor: 25789002048787408142851986929 (ECM curve 199, B1=250000, B2=25000000)
2^19727+1 has a factor: 504609870073241484856405169 (ECM curve 43, B1=250000, B2=25000000)
2^19727+1 has a factor: 9362694714595070850643845563 (ECM curve 44, B1=250000, B2=25000000)
2^19751+1 has a factor: 84927128446085971 (ECM curve 5, B1=250000, B2=25000000)
2^19753+1 has a factor: 173073547980056272180304892433 (ECM curve 549, B1=250000, B2=25000000)
2^19759+1 has a factor: 409465006747603120121443367371 (ECM curve 278, B1=250000, B2=25000000)
2^19861+1 has a factor: 29745181723602905627546617 (ECM curve 78, B1=250000, B2=25000000)
2^19861+1 has a factor: 43210605953702291637521 (ECM curve 6, B1=250000, B2=25000000)
2^19867+1 has a factor: 24004452422643472097 (ECM curve 5, B1=250000, B2=25000000)
2^19913+1 has a factor: 4012369753929857509129 (ECM curve 28, B1=250000, B2=25000000)
2^19919+1 has a factor: 201432145246062467506267 (ECM curve 70, B1=250000, B2=25000000)
2^19919+1 has a factor: 274481730912217874690732257 (ECM curve 43, B1=250000, B2=25000000)
2^19927+1 has a factor: 517271797710511284773867 (ECM curve 139, B1=250000, B2=25000000)
2^19963+1 has a factor: 3732554851977901456514111603 (ECM curve 5, B1=250000, B2=25000000)
2^19973+1 has a factor: 11573434450400809214978203 (ECM curve 61, B1=250000, B2=25000000)
2^19973+1 has a factor: 56073740730915797980771987 (ECM curve 69, B1=250000, B2=25000000)
2^19991+1 has a factor: 35960107478754457 (ECM curve 1, B1=250000, B2=25000000)

[/CODE]

pinhodecarlos 2018-10-10 20:22

Is there an automate way to report the factors to factordb?

GP2 2018-10-10 23:01

[QUOTE=pinhodecarlos;497805]Is there an automate way to report the factors to factordb?[/QUOTE]

If you go to FactorDB.com, then click on "Report results", then click on "Report factors", then you can just enter a bunch of lines of the form:

2^19507+1=1234449887923479271291136873
2^19507+1=844428452139314289368892697
etc.

In other words, the same as your "has a factor" lines, except slightly transformed. If you know how to use a Linux utility like [c]sed[/c] it is fairly straightforward.

pinhodecarlos 2018-10-11 07:56

[QUOTE=GP2;497818]If you go to FactorDB.com, then click on "Report results", then click on "Report factors", then you can just enter a bunch of lines of the form:

2^19507+1=1234449887923479271291136873
2^19507+1=844428452139314289368892697
etc.

In other words, the same as your "has a factor" lines, except slightly transformed. If you know how to use a Linux utility like [c]sed[/c] it is fairly straightforward.[/QUOTE]

I thought the report system would parse the results as I’ve posted before but I’ll then clean it using excel later on. Thank you a bunch!

GP2 2018-10-11 11:26

[QUOTE=pinhodecarlos;497838]I thought the report system would parse the results as I’ve posted before but I’ll then clean it using excel later on. Thank you a bunch![/QUOTE]

I went ahead and posted these factors to FactorDB myself. But the syntax will be useful for future reference.

PS, if you are posting Mersenne factors then you can just say M...=... instead of 2^...-1=... However this is usually unnecessary, since someone else will usually update FactorDB within a few days or weeks.

axn 2018-10-12 16:28

[QUOTE=pinhodecarlos;497063]2^19379+1 has a factor: 50661292745468868151307 (ECM curve 10, B1=250000, B2=25000000)
Cofactor is a probable prime!


[URL="http://factordb.com/index.php?query=2%5E19379%2B1"]http://factordb.com/index.php?query=2%5E19379%2B1[/URL]


P5804 [URL]http://factordb.com/index.php?id=1100000001172464482[/URL][/QUOTE]
This is now proven.

axn 2018-10-13 07:08

27000-29000
[CODE]2^27011+1 has a factor: 1903610316960942888315574129 (ECM curve 531, B1=250000, B2=25000000)
2^27011+1 has a factor: 23189246887553 (ECM curve 1, B1=250000, B2=25000000)
2^27011+1 has a factor: 4961116988666973054144899 (ECM curve 37, B1=250000, B2=25000000)
2^27043+1 has a factor: 14547281094122942731 (ECM curve 5, B1=250000, B2=25000000)
2^27059+1 has a factor: 26147954349391574521793 (ECM curve 104, B1=250000, B2=25000000)
2^27061+1 has a factor: 138426756961 (ECM curve 1, B1=250000, B2=25000000)
2^27061+1 has a factor: 20928339648263616433 (ECM curve 23, B1=250000, B2=25000000)
2^27073+1 has a factor: 126372628003247488843 (ECM curve 12, B1=250000, B2=25000000)
2^27077+1 has a factor: 2260303682609784593215755815387 (ECM curve 366, B1=250000, B2=25000000)
2^27077+1 has a factor: 24469799483244094937 (ECM curve 1, B1=250000, B2=25000000)
2^27107+1 has a factor: 3036937637045116032691 (ECM curve 5, B1=250000, B2=25000000)
2^27109+1 has a factor: 54869629613655555850175129657 (ECM curve 266, B1=250000, B2=25000000)
2^27109+1 has a factor: 6712915474051870954508633 (ECM curve 58, B1=250000, B2=25000000)
2^27109+1 has a factor: 934213997973975217 (ECM curve 4, B1=250000, B2=25000000)
2^27143+1 has a factor: 662740164267009584908661659 (ECM curve 178, B1=250000, B2=25000000)
2^27191+1 has a factor: 1045061363950639624251508091 (ECM curve 558, B1=250000, B2=25000000)
2^27191+1 has a factor: 866859227592628852331 (ECM curve 6, B1=250000, B2=25000000)
2^27197+1 has a factor: 6819701890455145634295687611 (ECM curve 1, B1=250000, B2=25000000)
2^27253+1 has a factor: 185212774325127395129 (ECM curve 1, B1=250000, B2=25000000)
2^27259+1 has a factor: 1795652823841 (ECM curve 1, B1=250000, B2=25000000)
2^27271+1 has a factor: 44842622438071273481 (ECM curve 9, B1=250000, B2=25000000)
2^27361+1 has a factor: 881944612927159720925547019 (ECM curve 73, B1=250000, B2=25000000)
2^27367+1 has a factor: 2085299627902245649633 (ECM curve 13, B1=250000, B2=25000000)
2^27407+1 has a factor: 1800642347001051787 (ECM curve 2, B1=250000, B2=25000000)
2^27427+1 has a factor: 1050861838601785907387 (ECM curve 8, B1=250000, B2=25000000)
2^27427+1 has a factor: 17095595924747909635897 (ECM curve 10, B1=250000, B2=25000000)
2^27427+1 has a factor: 498503497697 (ECM curve 1, B1=250000, B2=25000000)
2^27431+1 has a factor: 29310078777389728441526603 (ECM curve 45, B1=250000, B2=25000000)
2^27431+1 has a factor: 75423037225043 (ECM curve 5, B1=250000, B2=25000000)
2^27431+1 has a factor: 804542094697685291 (ECM curve 11, B1=250000, B2=25000000)
2^27457+1 has a factor: 1088214604336430953 (ECM curve 3, B1=250000, B2=25000000)
2^27481+1 has a factor: 1398692771608047067081 (ECM curve 14, B1=250000, B2=25000000)
2^27481+1 has a factor: 23707670320131450041 (ECM curve 1, B1=250000, B2=25000000)
2^27481+1 has a factor: 23910096812525347427 (ECM curve 5, B1=250000, B2=25000000)
2^27481+1 has a factor: 337044381648184876048867507 (ECM curve 1, B1=250000, B2=25000000) composite
2^27481+1 has a factor: 6453723112305155576786085523969 (ECM curve 310, B1=250000, B2=25000000)
2^27487+1 has a factor: 1627482256972515899 (ECM curve 32, B1=250000, B2=25000000)
2^27487+1 has a factor: 37831128560611 (ECM curve 2, B1=250000, B2=25000000)
2^27509+1 has a factor: 103813824569634556922252584483 (ECM curve 533, B1=250000, B2=25000000)
2^27529+1 has a factor: 1423023341969 (ECM curve 2, B1=250000, B2=25000000)
2^27539+1 has a factor: 22840475520031822108679579 (ECM curve 348, B1=250000, B2=25000000)
2^27539+1 has a factor: 49583910870484418009 (ECM curve 1, B1=250000, B2=25000000)
2^27539+1 has a factor: 71505509951698723597932707 (ECM curve 6, B1=250000, B2=25000000)
2^27551+1 has a factor: 6187201551503963662159217 (ECM curve 91, B1=250000, B2=25000000)
2^27551+1 has a factor: 747966732595057 (ECM curve 1, B1=250000, B2=25000000)
2^27581+1 has a factor: 38185727611132421311159200811 (ECM curve 291, B1=250000, B2=25000000)
2^27583+1 has a factor: 1484725428766700843 (ECM curve 6, B1=250000, B2=25000000)
2^27611+1 has a factor: 58899530714960493528587657 (ECM curve 155, B1=250000, B2=25000000)
2^27617+1 has a factor: 114926665638273097670441 (ECM curve 75, B1=250000, B2=25000000)
2^27617+1 has a factor: 160716057696888648262742809 (ECM curve 14, B1=250000, B2=25000000)
2^27617+1 has a factor: 243492019049 (ECM curve 8, B1=250000, B2=25000000)
2^27617+1 has a factor: 3017741633758590659 (ECM curve 1, B1=250000, B2=25000000)
2^27647+1 has a factor: 16183901140959300453713 (ECM curve 4, B1=250000, B2=25000000)
2^27647+1 has a factor: 20232987275960190387815395283 (ECM curve 171, B1=250000, B2=25000000)
2^27647+1 has a factor: 900125175270055329486809 (ECM curve 8, B1=250000, B2=25000000)
2^27691+1 has a factor: 5676688250023633 (ECM curve 1, B1=250000, B2=25000000)
2^27691+1 has a factor: 756954202057710272459 (ECM curve 2, B1=250000, B2=25000000)
2^27701+1 has a factor: 4672559573017988146321 (ECM curve 13, B1=250000, B2=25000000)
2^27733+1 has a factor: 113932037259153197053498407803 (ECM curve 380, B1=250000, B2=25000000)
2^27733+1 has a factor: 8302428344810133633353 (ECM curve 54, B1=250000, B2=25000000)
2^27737+1 has a factor: 163015967937987660496657 (ECM curve 44, B1=250000, B2=25000000)
2^27737+1 has a factor: 4101333003137327664894994531 (ECM curve 81, B1=250000, B2=25000000)
2^27739+1 has a factor: 279788798546110090324939 (ECM curve 52, B1=250000, B2=25000000)
2^27739+1 has a factor: 4055967776210747 (ECM curve 3, B1=250000, B2=25000000)
2^27749+1 has a factor: 2315025214766991156546378643 (ECM curve 283, B1=250000, B2=25000000)
2^27749+1 has a factor: 77555624603 (ECM curve 1, B1=250000, B2=25000000)
2^27767+1 has a factor: 625295031934666211933761 (ECM curve 15, B1=250000, B2=25000000)
2^27779+1 has a factor: 1101122845793569901540881 (ECM curve 85, B1=250000, B2=25000000)
2^27779+1 has a factor: 36265571311097299 (ECM curve 4, B1=250000, B2=25000000)
2^27791+1 has a factor: 16951291649328720379 (ECM curve 8, B1=250000, B2=25000000)
2^27793+1 has a factor: 5418347975374571 (ECM curve 6, B1=250000, B2=25000000)
2^27823+1 has a factor: 50540906861281 (ECM curve 4, B1=250000, B2=25000000)
2^27827+1 has a factor: 416387478059387420883095729113 (ECM curve 486, B1=250000, B2=25000000)
2^27847+1 has a factor: 2606231094638456225716306873 (ECM curve 336, B1=250000, B2=25000000)
2^27847+1 has a factor: 56737537085651 (ECM curve 1, B1=250000, B2=25000000)
2^27851+1 has a factor: 19143277194429270979 (ECM curve 3, B1=250000, B2=25000000)
2^27851+1 has a factor: 3552852115430344058443 (ECM curve 26, B1=250000, B2=25000000)
2^27851+1 has a factor: 675359167074022316975897 (ECM curve 9, B1=250000, B2=25000000)
2^27883+1 has a factor: 272055716517833 (ECM curve 1, B1=250000, B2=25000000)
2^27883+1 has a factor: 4586582959297918444259 (ECM curve 21, B1=250000, B2=25000000)
2^27901+1 has a factor: 610835875609489 (ECM curve 1, B1=250000, B2=25000000)
2^27943+1 has a factor: 4562924099947011425441 (ECM curve 3, B1=250000, B2=25000000)
2^27947+1 has a factor: 1095279751230775516419366493849 (ECM curve 484, B1=250000, B2=25000000)
2^27953+1 has a factor: 235650478390398067 (ECM curve 6, B1=250000, B2=25000000)
2^27953+1 has a factor: 851801519814235049836691 (ECM curve 155, B1=250000, B2=25000000)
2^27961+1 has a factor: 19575462969743444837717689 (ECM curve 176, B1=250000, B2=25000000)
2^27961+1 has a factor: 81660719698857910993 (ECM curve 9, B1=250000, B2=25000000)
2^28001+1 has a factor: 6153515811016502959831249 (ECM curve 150, B1=250000, B2=25000000)
2^28001+1 has a factor: 933941724398377 (ECM curve 1, B1=250000, B2=25000000)
2^28019+1 has a factor: 436554560508529 (ECM curve 7, B1=250000, B2=25000000)
2^28081+1 has a factor: 194074572623023224521 (ECM curve 36, B1=250000, B2=25000000)
2^28097+1 has a factor: 64437390322933682605662763 (ECM curve 433, B1=250000, B2=25000000)
2^28109+1 has a factor: 1965566999081613689 (ECM curve 10, B1=250000, B2=25000000)
2^28151+1 has a factor: 13694309049729730986997426481 (ECM curve 477, B1=250000, B2=25000000)
2^28163+1 has a factor: 667910928085896083830211 (ECM curve 34, B1=250000, B2=25000000)
2^28181+1 has a factor: 11946314179933372023463201 (ECM curve 230, B1=250000, B2=25000000)
2^28181+1 has a factor: 3039495248907569 (ECM curve 2, B1=250000, B2=25000000)
2^28181+1 has a factor: 47384740646293423216952742803233 (ECM curve 97, B1=250000, B2=25000000)
2^28201+1 has a factor: 150365118171363929 (ECM curve 5, B1=250000, B2=25000000)
2^28219+1 has a factor: 28713532419998629184239387 (ECM curve 10, B1=250000, B2=25000000)
2^28279+1 has a factor: 48698228930129950841747255281 (ECM curve 85, B1=250000, B2=25000000)
2^28279+1 has a factor: 509174446754221300105627547 (ECM curve 39, B1=250000, B2=25000000)
2^28283+1 has a factor: 210778685447316881 (ECM curve 3, B1=250000, B2=25000000)
2^28283+1 has a factor: 228720017516915073187 (ECM curve 1, B1=250000, B2=25000000)
2^28283+1 has a factor: 2718776596724751713 (ECM curve 6, B1=250000, B2=25000000)
2^28289+1 has a factor: 10065835336874254827641 (ECM curve 15, B1=250000, B2=25000000)
2^28289+1 has a factor: 421525369211051291 (ECM curve 2, B1=250000, B2=25000000)
2^28307+1 has a factor: 60842159977 (ECM curve 1, B1=250000, B2=25000000)
2^28309+1 has a factor: 5934232433798148501779590667 (ECM curve 112, B1=250000, B2=25000000)
2^28349+1 has a factor: 41358827553340249703809 (ECM curve 21, B1=250000, B2=25000000)
2^28351+1 has a factor: 274689285332966958242531 (ECM curve 6, B1=250000, B2=25000000)
2^28403+1 has a factor: 92516492483089 (ECM curve 2, B1=250000, B2=25000000)
2^28411+1 has a factor: 2252118748676511340349051 (ECM curve 42, B1=250000, B2=25000000)
2^28411+1 has a factor: 269475834833 (ECM curve 1, B1=250000, B2=25000000)
2^28411+1 has a factor: 95761571850668033 (ECM curve 10, B1=250000, B2=25000000)
2^28439+1 has a factor: 170415304091 (ECM curve 3, B1=250000, B2=25000000)
2^28447+1 has a factor: 1365094655402217064345563419 (ECM curve 240, B1=250000, B2=25000000)
2^28447+1 has a factor: 29004703681830150180228293371 (ECM curve 50, B1=250000, B2=25000000)
2^28463+1 has a factor: 18640106517380667921643 (ECM curve 64, B1=250000, B2=25000000)
2^28493+1 has a factor: 157815186961901081661428683393 (ECM curve 366, B1=250000, B2=25000000)
2^28493+1 has a factor: 32481658787556821641 (ECM curve 3, B1=250000, B2=25000000)
2^28513+1 has a factor: 4024867316598723881630089 (ECM curve 94, B1=250000, B2=25000000)
2^28541+1 has a factor: 1016010220540673320339214587 (ECM curve 50, B1=250000, B2=25000000)
2^28547+1 has a factor: 220647021166968407390033 (ECM curve 212, B1=250000, B2=25000000)
2^28559+1 has a factor: 69421784803803132180707 (ECM curve 28, B1=250000, B2=25000000)
2^28573+1 has a factor: 24381033825210616972198883 (ECM curve 1, B1=250000, B2=25000000) composite
2^28573+1 has a factor: 46876004039401483 (ECM curve 2, B1=250000, B2=25000000)
2^28579+1 has a factor: 146143403025640956497 (ECM curve 10, B1=250000, B2=25000000)
2^28579+1 has a factor: 18524225464144344134867 (ECM curve 9, B1=250000, B2=25000000)
2^28579+1 has a factor: 21441171692020667003 (ECM curve 2, B1=250000, B2=25000000)
2^28579+1 has a factor: 8561341062910033297 (ECM curve 26, B1=250000, B2=25000000)
2^28591+1 has a factor: 223724822213254274858003 (ECM curve 2, B1=250000, B2=25000000)
2^28597+1 has a factor: 131493212322034723 (ECM curve 3, B1=250000, B2=25000000)
2^28597+1 has a factor: 1716640697753906747 (ECM curve 2, B1=250000, B2=25000000)
2^28597+1 has a factor: 2960283919601207732339 (ECM curve 14, B1=250000, B2=25000000)
2^28603+1 has a factor: 56846463124758117772993 (ECM curve 100, B1=250000, B2=25000000)
2^28607+1 has a factor: 20707025618971 (ECM curve 2, B1=250000, B2=25000000)
2^28627+1 has a factor: 34547112988287842482503211 (ECM curve 95, B1=250000, B2=25000000)
2^28643+1 has a factor: 2388511982578324047444253363 (ECM curve 416, B1=250000, B2=25000000)
2^28643+1 has a factor: 3472402000230168311687449339 (ECM curve 1, B1=250000, B2=25000000) composite
2^28649+1 has a factor: 62447685671359916646584611 (ECM curve 199, B1=250000, B2=25000000)
2^28657+1 has a factor: 415574479471395771322801 (ECM curve 74, B1=250000, B2=25000000)
2^28661+1 has a factor: 365628140906440562987 (ECM curve 19, B1=250000, B2=25000000)
2^28723+1 has a factor: 6258292967953672691 (ECM curve 2, B1=250000, B2=25000000)
2^28729+1 has a factor: 7237219556729495628854827 (ECM curve 3, B1=250000, B2=25000000)
2^28753+1 has a factor: 646592460979 (ECM curve 1, B1=250000, B2=25000000)
2^28771+1 has a factor: 130198154347 (ECM curve 1, B1=250000, B2=25000000)
2^28771+1 has a factor: 356749065607009 (ECM curve 2, B1=250000, B2=25000000)
2^28771+1 has a factor: 8023105255397109961 (ECM curve 11, B1=250000, B2=25000000)
2^28807+1 has a factor: 77580221183017411060663369 (ECM curve 138, B1=250000, B2=25000000)
2^28837+1 has a factor: 14187276381204655766404013833 (ECM curve 340, B1=250000, B2=25000000)
2^28837+1 has a factor: 19391806598969947 (ECM curve 3, B1=250000, B2=25000000)
2^28837+1 has a factor: 56900098706076523 (ECM curve 2, B1=250000, B2=25000000)
2^28859+1 has a factor: 7009966665910895841899 (ECM curve 14, B1=250000, B2=25000000)
2^28901+1 has a factor: 113821643712307 (ECM curve 1, B1=250000, B2=25000000)
2^28901+1 has a factor: 1901561348883683 (ECM curve 1, B1=250000, B2=25000000)
2^28901+1 has a factor: 301636854721997849 (ECM curve 1, B1=250000, B2=25000000)
2^28901+1 has a factor: 55622835362823569 (ECM curve 2, B1=250000, B2=25000000)
2^28909+1 has a factor: 659215419859444859 (ECM curve 2, B1=250000, B2=25000000)
2^28921+1 has a factor: 205190087034707 (ECM curve 2, B1=250000, B2=25000000)
2^28949+1 has a factor: 6788545022510280233 (ECM curve 2, B1=250000, B2=25000000)
2^28949+1 has a factor: 8539203723386733298451622179 (ECM curve 288, B1=250000, B2=25000000)
2^28961+1 has a factor: 114776310394019 (ECM curve 2, B1=250000, B2=25000000)
2^28979+1 has a factor: 1623772991294049131 (ECM curve 2, B1=250000, B2=25000000)
2^28979+1 has a factor: 358451810279967656249 (ECM curve 8, B1=250000, B2=25000000)
2^28979+1 has a factor: 383496358583200558793 (ECM curve 16, B1=250000, B2=25000000)
2^28979+1 has a factor: 87223504706485431107 (ECM curve 5, B1=250000, B2=25000000)
[/CODE]
Three of the factors are in fact composite.

And then, at the beginning of the new range:
[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

paulunderwood 2018-10-13 10:16

[QUOTE=axn;497976]

And then, at the beginning of the new range:
[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]

My test:

[CODE]time ./pfgw64 -k -f0 -od -q"(2^29027+1)/3/578914489/275322488297" | ../../coding/gwnum/hybrid - 1 2 29027 1
Testing (x + 2)^(n + 1) == 5 (mod n, x^2 + 1)...
Likely prime!

real 0m0.392s
user 0m0.448s
sys 0m0.008s
[/CODE]

Congrats :toot:

axn 2018-10-14 17:37

[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

paulunderwood 2018-10-14 18:21

[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]

[CODE]time ./pfgw64 -k -f0 -od -q"(2^29437+1)/3/1177481/24192412837755888627020059" | ../../coding/gwnum/hybrid - 1 2 29437 1

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

real 0m0.838s
user 0m0.468s
sys 0m0.012s
[/CODE]

Congrats again! :toot: :toot:

axn 2018-10-15 05:29

26500-27000
[CODE]2^26539+1 has a factor: 1755924601699214344410667 (ECM curve 3, B1=250000, B2=25000000)
2^26539+1 has a factor: 7268077218028488681696570091 (ECM curve 142, B1=250000, B2=25000000)
2^26539+1 has a factor: 739022880529378374010651 (ECM curve 27, B1=250000, B2=25000000)
2^26557+1 has a factor: 570786105385334328589929220091 (ECM curve 546, B1=250000, B2=25000000)
2^26633+1 has a factor: 521962997722546931 (ECM curve 2, B1=250000, B2=25000000)
2^26633+1 has a factor: 951800423694101064571 (ECM curve 1, B1=250000, B2=25000000)
2^26647+1 has a factor: 23841269366857 (ECM curve 5, B1=250000, B2=25000000)
2^26647+1 has a factor: 28874286387802821924988027 (ECM curve 160, B1=250000, B2=25000000)
2^26669+1 has a factor: 34208848866592401191347 (ECM curve 1, B1=250000, B2=25000000)
2^26681+1 has a factor: 4315804405640649719929 (ECM curve 10, B1=250000, B2=25000000)
2^26687+1 has a factor: 16977818615058478249 (ECM curve 2, B1=250000, B2=25000000)
2^26699+1 has a factor: 157529185452510481 (ECM curve 7, B1=250000, B2=25000000)
2^26711+1 has a factor: 1457750207323 (ECM curve 1, B1=250000, B2=25000000)
2^26723+1 has a factor: 1012492621354433 (ECM curve 3, B1=250000, B2=25000000)
2^26723+1 has a factor: 10812728119454580422377 (ECM curve 17, B1=250000, B2=25000000)
2^26731+1 has a factor: 6908238573941584112221819 (ECM curve 96, B1=250000, B2=25000000)
2^26737+1 has a factor: 126642046409 (ECM curve 1, B1=250000, B2=25000000)
2^26737+1 has a factor: 99279086020459 (ECM curve 2, B1=250000, B2=25000000)
2^26759+1 has a factor: 10004671701816244027 (ECM curve 4, B1=250000, B2=25000000)
2^26777+1 has a factor: 12131552851519531053693931 (ECM curve 57, B1=250000, B2=25000000)
2^26783+1 has a factor: 10109260419930531745284947 (ECM curve 2, B1=250000, B2=25000000)
2^26813+1 has a factor: 152204642178717843374227 (ECM curve 11, B1=250000, B2=25000000)
2^26813+1 has a factor: 4705462567347407936404121 (ECM curve 11, B1=250000, B2=25000000)
2^26821+1 has a factor: 116252091047819 (ECM curve 2, B1=250000, B2=25000000)
2^26821+1 has a factor: 45301956409 (ECM curve 1, B1=250000, B2=25000000)
2^26833+1 has a factor: 464561562188754187 (ECM curve 4, B1=250000, B2=25000000)
2^26849+1 has a factor: 189072669037665312997283 (ECM curve 10, B1=250000, B2=25000000)
2^26849+1 has a factor: 722900745644870559910094005979 (ECM curve 52, B1=250000, B2=25000000)
2^26881+1 has a factor: 2602953739254332171 (ECM curve 1, B1=250000, B2=25000000)
2^26921+1 has a factor: 780506703854206080715456219 (ECM curve 133, B1=250000, B2=25000000)
2^26951+1 has a factor: 342613870591026181147691 (ECM curve 117, B1=250000, B2=25000000)
2^26951+1 has a factor: 40752350971465158097 (ECM curve 6, B1=250000, B2=25000000)
2^26953+1 has a factor: 18064169244917387 (ECM curve 13, B1=250000, B2=25000000)
2^26953+1 has a factor: 191735787203823394339 (ECM curve 7, B1=250000, B2=25000000)
2^26959+1 has a factor: 3132242978151222331461052457 (ECM curve 427, B1=250000, B2=25000000)
2^26987+1 has a factor: 123185407029083981129 (ECM curve 4, B1=250000, B2=25000000)
2^26993+1 has a factor: 2064939720250565676834316337 (ECM curve 22, B1=250000, B2=25000000)
2^26993+1 has a factor: 211389047300574330083555495321 (ECM curve 192, B1=250000, B2=25000000)
2^26993+1 has a factor: 28444224652867888762897 (ECM curve 20, B1=250000, B2=25000000)
2^26993+1 has a factor: 6069686027407845098070931976089 (ECM curve 1, B1=250000, B2=25000000)
2^26993+1 has a factor: 660639476683 (ECM curve 1, B1=250000, B2=25000000)
2^26993+1 has a factor: 7351898822208558748363 (ECM curve 7, B1=250000, B2=25000000)
[/CODE]

GP2 2018-10-19 02:42

Status update: [URL="http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/"]Wagstaff page[/URL]

The page contains downloadable links to factors and PRP residues.

Using the Gerbicz cofactor compositeness test, I didn't find any new PRP cofactors in the range 1M to 2M, with the present set of known factors. So the largest known PRP cofactor is still the one for the exponent 823337.

Below 2M, I did PRP tests for all exponents. Above 2M, I'm currently only doing PRP tests for exponents with no known factors, and therefore won't find any new PRP cofactors.

I'm currently partway through the 4M range. Still verifying the small exponent ranges, but might switch to the 10M range at some point. But first I'd want to factor those higher ranges a bit more, possibly if I get a RTX 2080 for that purpose.

The previous efforts in 2013, which used the (unproven) Vrba-Reix algorithm in the LLR program, halted at 10M. Ryan Propper found the Wagstaff (probable) primes 13347311
13372531 in September 2013, but it's not known how thoroughly he searched the space above 10M.

The PRP testing will probably get interrupted temporarily at some point for the year-end holiday season, when spot instance prices in the cloud tend to spike.

axn 2018-10-19 03:25

[QUOTE=GP2;498262]I'm currently partway through the 4M range. Still verifying the small exponent ranges, but might switch to the 10M range at some point. But first I'd want to factor those higher ranges a bit more, possibly if I get a RTX 2080 for that purpose.[/QUOTE]
If you can hook me up with instruction to compile mfatktc Wagstaff and worktodo files, I can put a 1050Ti for this. I can also throw in couple of slow cores for P-1

GP2 2018-10-19 04:00

[QUOTE=axn;498265]If you can hook me up with instruction to compile mfatktc Wagstaff and worktodo files, I can put a 1050Ti for this. I can also throw in couple of slow cores for P-1[/QUOTE]

It's quite simple really. Just uncomment the line [c]#define WAGSTAFF[/c] in the [c]params.h[/c] file, and then compile mfaktc in the usual way. The worktodo lines are exactly the same, it's the executable that reads them which is different.

I am doing some minimal P−1 myself, with bounds B1 = p / 200 and B2 = p / 10, which actually finds factors for a surprising percentage of exponents. For P−1, as with TF, there is a lot of very low-hanging fruit but then rapidly diminishing returns.

I already TF'd the 10M range from 60–64. Back in 2013, ATH TF'd everything from 8M to 16M to 60 bits (and 10k to 1M to 56 bits, 1M to 2M to 57 bits, 2M to 4M to 58 bits, 4M to 8M to 59 bits, 16M to 32M to 61 bits, 32M to 50M to 62 bits).

axn 2018-10-19 04:16

[QUOTE=GP2;498269]It's quite simple really. Just uncomment the line [c]#define WAGSTAFF[/c] in the [c]params.h[/c] file, and then compile mfaktc in the usual way. [/quote]
Cool. Let me try that out.
[QUOTE=GP2;498269]The worktodo lines are exactly the same, it's the executable that reads them which is different.[/quote]
Yes, but I will still need a list of unfactored exponents and the bit levels. Do you have that handy at your site (haven't downloaded any files yet).

axn 2018-10-19 11:39

29000-31000
[CODE]2^29017+1 has a factor: 10985215274787989112855073 (ECM curve 192, B1=250000, B2=25000000)
2^29017+1 has a factor: 5983695326673366064937939 (ECM curve 21, B1=250000, B2=25000000)
2^29023+1 has a factor: 35846157014736381683 (ECM curve 1, B1=250000, B2=25000000)
2^29023+1 has a factor: 4578787486147652969 (ECM curve 6, B1=250000, B2=25000000)
2^29027+1 has a factor: 275322488297 (ECM curve 1, B1=250000, B2=25000000)
2^29059+1 has a factor: 299447655126598977294353329 (ECM curve 104, B1=250000, B2=25000000)
2^29077+1 has a factor: 135404152544693679091 (ECM curve 5, B1=250000, B2=25000000)
2^29101+1 has a factor: 16766968794294002128012409 (ECM curve 28, B1=250000, B2=25000000)
2^29101+1 has a factor: 3237163110420283873 (ECM curve 15, B1=250000, B2=25000000)
2^29129+1 has a factor: 397023395314465007305145041 (ECM curve 153, B1=250000, B2=25000000)
2^29131+1 has a factor: 27660723419518695971539 (ECM curve 31, B1=250000, B2=25000000)
2^29147+1 has a factor: 168474526268598481261898411 (ECM curve 95, B1=250000, B2=25000000)
2^29147+1 has a factor: 333612445869769803619891 (ECM curve 83, B1=250000, B2=25000000)
2^29153+1 has a factor: 2837799453631615157449 (ECM curve 4, B1=250000, B2=25000000)
2^29167+1 has a factor: 81476296422691496827 (ECM curve 7, B1=250000, B2=25000000)
2^29207+1 has a factor: 194309340739603939417578628987 (ECM curve 81, B1=250000, B2=25000000)
2^29207+1 has a factor: 20015596640845499 (ECM curve 14, B1=250000, B2=25000000)
2^29209+1 has a factor: 193874679083 (ECM curve 1, B1=250000, B2=25000000)
2^29209+1 has a factor: 385264283146979728889 (ECM curve 3, B1=250000, B2=25000000)
2^29209+1 has a factor: 93880926686292931 (ECM curve 1, B1=250000, B2=25000000)
2^29243+1 has a factor: 45000473579 (ECM curve 1, B1=250000, B2=25000000)
2^29251+1 has a factor: 1319699822839113600611 (ECM curve 19, B1=250000, B2=25000000)
2^29287+1 has a factor: 2201930864186899619 (ECM curve 2, B1=250000, B2=25000000)
2^29297+1 has a factor: 10575333271053659 (ECM curve 1, B1=250000, B2=25000000)
2^29297+1 has a factor: 551594887191947 (ECM curve 1, B1=250000, B2=25000000)
2^29297+1 has a factor: 6124608939120889539384292001 (ECM curve 439, B1=250000, B2=25000000)
2^29303+1 has a factor: 14621525931673796670835123 (ECM curve 16, B1=250000, B2=25000000)
2^29347+1 has a factor: 56809139688120287737 (ECM curve 20, B1=250000, B2=25000000)
2^29363+1 has a factor: 54493251669377 (ECM curve 1, B1=250000, B2=25000000)
2^29401+1 has a factor: 19087949187259423702749593 (ECM curve 52, B1=250000, B2=25000000)
2^29423+1 has a factor: 15849379386299 (ECM curve 4, B1=250000, B2=25000000)
2^29423+1 has a factor: 29890768207459 (ECM curve 1, B1=250000, B2=25000000)
2^29437+1 has a factor: 24192412837755888627020059 (ECM curve 390, B1=250000, B2=25000000)
2^29453+1 has a factor: 43960596434043613913 (ECM curve 9, B1=250000, B2=25000000)
2^29473+1 has a factor: 1402827858578633009 (ECM curve 4, B1=250000, B2=25000000)
2^29501+1 has a factor: 127383181321219667 (ECM curve 9, B1=250000, B2=25000000)
2^29501+1 has a factor: 219432943723714144993536403 (ECM curve 155, B1=250000, B2=25000000)
2^29537+1 has a factor: 633009030520394393 (ECM curve 2, B1=250000, B2=25000000)
2^29569+1 has a factor: 442962880300393 (ECM curve 1, B1=250000, B2=25000000)
2^29569+1 has a factor: 6754969324047381395176441 (ECM curve 37, B1=250000, B2=25000000)
2^29573+1 has a factor: 143336431975731913 (ECM curve 4, B1=250000, B2=25000000)
2^29629+1 has a factor: 1043355902291 (ECM curve 3, B1=250000, B2=25000000)
2^29629+1 has a factor: 11235677803531657805802059 (ECM curve 82, B1=250000, B2=25000000)
2^29629+1 has a factor: 93323431709009 (ECM curve 2, B1=250000, B2=25000000)
2^29633+1 has a factor: 284039485439214183739843 (ECM curve 34, B1=250000, B2=25000000)
2^29641+1 has a factor: 4346563900126844270041 (ECM curve 2, B1=250000, B2=25000000)
2^29641+1 has a factor: 49479025072103267772889 (ECM curve 58, B1=250000, B2=25000000)
2^29663+1 has a factor: 8155912993235371563955498777 (ECM curve 150, B1=250000, B2=25000000)
2^29671+1 has a factor: 166668268013508464258664299 (ECM curve 1, B1=250000, B2=25000000)
2^29683+1 has a factor: 384654752626387 (ECM curve 3, B1=250000, B2=25000000)
2^29717+1 has a factor: 2138401518313953721 (ECM curve 7, B1=250000, B2=25000000)
2^29723+1 has a factor: 153146780613597142093910202499 (ECM curve 275, B1=250000, B2=25000000)
2^29759+1 has a factor: 3164814707948273197677811177 (ECM curve 26, B1=250000, B2=25000000)
2^29761+1 has a factor: 6104392593146239963 (ECM curve 4, B1=250000, B2=25000000)
2^29789+1 has a factor: 10032848337661364958619 (ECM curve 23, B1=250000, B2=25000000)
2^29789+1 has a factor: 2232589416868335641 (ECM curve 8, B1=250000, B2=25000000)
2^29803+1 has a factor: 4972606821805097 (ECM curve 2, B1=250000, B2=25000000)
2^29851+1 has a factor: 1044882388469587 (ECM curve 3, B1=250000, B2=25000000)
2^29873+1 has a factor: 1046109867030087146080697 (ECM curve 8, B1=250000, B2=25000000)
2^29879+1 has a factor: 312941192364808990753 (ECM curve 7, B1=250000, B2=25000000)
2^29881+1 has a factor: 30981855692402526925451 (ECM curve 20, B1=250000, B2=25000000)
2^29881+1 has a factor: 6568941090083 (ECM curve 2, B1=250000, B2=25000000)
2^29917+1 has a factor: 1759474651844633 (ECM curve 1, B1=250000, B2=25000000)
2^29921+1 has a factor: 301787121641587 (ECM curve 4, B1=250000, B2=25000000)
2^29927+1 has a factor: 5015832812973114642002833 (ECM curve 87, B1=250000, B2=25000000)
2^29947+1 has a factor: 235838406563676420269206526627 (ECM curve 541, B1=250000, B2=25000000)
2^29959+1 has a factor: 7665172168273 (ECM curve 1, B1=250000, B2=25000000)
2^29983+1 has a factor: 1108738617753121 (ECM curve 3, B1=250000, B2=25000000)
2^29983+1 has a factor: 32349226737465996041 (ECM curve 1, B1=250000, B2=25000000)
2^29989+1 has a factor: 8759572996859921 (ECM curve 2, B1=250000, B2=25000000)
2^30011+1 has a factor: 176087176539599161 (ECM curve 17, B1=250000, B2=25000000)
2^30011+1 has a factor: 347846697041 (ECM curve 1, B1=250000, B2=25000000)
2^30013+1 has a factor: 14815571496036431218644851 (ECM curve 1, B1=250000, B2=25000000)
2^30029+1 has a factor: 123981701998930379 (ECM curve 2, B1=250000, B2=25000000)
2^30029+1 has a factor: 1941934401862472333094699979609 (ECM curve 237, B1=250000, B2=25000000)
2^30029+1 has a factor: 4261021138539264929 (ECM curve 6, B1=250000, B2=25000000)
2^30047+1 has a factor: 388682191667027 (ECM curve 4, B1=250000, B2=25000000)
2^30071+1 has a factor: 139431005599134140916587 (ECM curve 9, B1=250000, B2=25000000)
2^30089+1 has a factor: 76249383316898708051 (ECM curve 14, B1=250000, B2=25000000)
2^30097+1 has a factor: 6359957879959193700721 (ECM curve 19, B1=250000, B2=25000000)
2^30103+1 has a factor: 1800535266059 (ECM curve 2, B1=250000, B2=25000000)
2^30109+1 has a factor: 3517289842387 (ECM curve 2, B1=250000, B2=25000000)
2^30133+1 has a factor: 1199773708095109623368356339 (ECM curve 180, B1=250000, B2=25000000)
2^30137+1 has a factor: 38226452096017290827 (ECM curve 8, B1=250000, B2=25000000)
2^30139+1 has a factor: 360129645163 (ECM curve 1, B1=250000, B2=25000000)
2^30161+1 has a factor: 184411652963 (ECM curve 3, B1=250000, B2=25000000)
2^30181+1 has a factor: 11116835339793429962679632718209 (ECM curve 141, B1=250000, B2=25000000)
2^30181+1 has a factor: 2394746756771 (ECM curve 2, B1=250000, B2=25000000)
2^30187+1 has a factor: 6236810278572209861721306706107468361 (ECM curve 157, B1=250000, B2=25000000)
2^30203+1 has a factor: 136464526596172583161294046779 (ECM curve 69, B1=250000, B2=25000000)
2^30211+1 has a factor: 35203736505467 (ECM curve 1, B1=250000, B2=25000000)
2^30223+1 has a factor: 1094837380410697606621553 (ECM curve 43, B1=250000, B2=25000000)
2^30223+1 has a factor: 167371242193779202739734802177 (ECM curve 161, B1=250000, B2=25000000)
2^30223+1 has a factor: 1868193909403599851 (ECM curve 7, B1=250000, B2=25000000)
2^30241+1 has a factor: 23673100223152727690753 (ECM curve 13, B1=250000, B2=25000000)
2^30241+1 has a factor: 92764836558705398769142067 (ECM curve 54, B1=250000, B2=25000000)
2^30259+1 has a factor: 310897388588107 (ECM curve 5, B1=250000, B2=25000000)
2^30269+1 has a factor: 16703004363834641 (ECM curve 1, B1=250000, B2=25000000)
2^30269+1 has a factor: 563880347716891 (ECM curve 3, B1=250000, B2=25000000)
2^30313+1 has a factor: 153765570531383394448927033 (ECM curve 110, B1=250000, B2=25000000)
2^30431+1 has a factor: 11328270324497815441699 (ECM curve 2, B1=250000, B2=25000000)
2^30449+1 has a factor: 3533517067317910363 (ECM curve 4, B1=250000, B2=25000000)
2^30467+1 has a factor: 73242350124992002963291 (ECM curve 34, B1=250000, B2=25000000)
2^30469+1 has a factor: 313014472178604693639859 (ECM curve 131, B1=250000, B2=25000000)
2^30469+1 has a factor: 379626982051 (ECM curve 1, B1=250000, B2=25000000)
2^30469+1 has a factor: 606594177406443051728600331649 (ECM curve 227, B1=250000, B2=25000000)
2^30493+1 has a factor: 6140199770321 (ECM curve 1, B1=250000, B2=25000000)
2^30497+1 has a factor: 12428837124454681243 (ECM curve 1, B1=250000, B2=25000000)
2^30497+1 has a factor: 661977590597963 (ECM curve 2, B1=250000, B2=25000000)
2^30497+1 has a factor: 991525439898235579 (ECM curve 7, B1=250000, B2=25000000)
2^30529+1 has a factor: 929521379383607499673 (ECM curve 15, B1=250000, B2=25000000)
2^30539+1 has a factor: 726084974796392776129 (ECM curve 30, B1=250000, B2=25000000)
2^30577+1 has a factor: 287963594616870739755004651 (ECM curve 273, B1=250000, B2=25000000)
2^30593+1 has a factor: 647558089145304193 (ECM curve 1, B1=250000, B2=25000000)
2^30649+1 has a factor: 266269598124070300079466067 (ECM curve 78, B1=250000, B2=25000000)
2^30661+1 has a factor: 522848848771 (ECM curve 1, B1=250000, B2=25000000)
2^30677+1 has a factor: 17788006799462055467 (ECM curve 3, B1=250000, B2=25000000)
2^30689+1 has a factor: 4014428151379 (ECM curve 1, B1=250000, B2=25000000)
2^30697+1 has a factor: 1220302308265648721 (ECM curve 6, B1=250000, B2=25000000)
2^30697+1 has a factor: 1589838835081912191531601961 (ECM curve 1, B1=250000, B2=25000000)
2^30697+1 has a factor: 94033635087401 (ECM curve 2, B1=250000, B2=25000000)
2^30707+1 has a factor: 12244476466856899 (ECM curve 1, B1=250000, B2=25000000)
2^30707+1 has a factor: 378815752657231179780397141121 (ECM curve 324, B1=250000, B2=25000000)
2^30707+1 has a factor: 49273081396686139 (ECM curve 3, B1=250000, B2=25000000)
2^30707+1 has a factor: 87796717433 (ECM curve 1, B1=250000, B2=25000000)
2^30757+1 has a factor: 2067430104075313 (ECM curve 2, B1=250000, B2=25000000)
2^30763+1 has a factor: 39654865186451 (ECM curve 6, B1=250000, B2=25000000)
2^30773+1 has a factor: 7647424797898886253016566573949441 (ECM curve 535, B1=250000, B2=25000000)
2^30781+1 has a factor: 60270223835066651948102849 (ECM curve 82, B1=250000, B2=25000000)
2^30809+1 has a factor: 2773572678273833 (ECM curve 1, B1=250000, B2=25000000)
2^30809+1 has a factor: 61535324045850427 (ECM curve 1, B1=250000, B2=25000000)
2^30839+1 has a factor: 127989068865503807343464009 (ECM curve 32, B1=250000, B2=25000000)
2^30841+1 has a factor: 2087962099897 (ECM curve 2, B1=250000, B2=25000000)
2^30851+1 has a factor: 233147362307 (ECM curve 2, B1=250000, B2=25000000)
2^30851+1 has a factor: 24678181305419 (ECM curve 3, B1=250000, B2=25000000)
2^30859+1 has a factor: 5863348236114644762512763 (ECM curve 105, B1=250000, B2=25000000)
2^30869+1 has a factor: 1555227834179033387 (ECM curve 4, B1=250000, B2=25000000)
2^30869+1 has a factor: 7054864973617 (ECM curve 3, B1=250000, B2=25000000)
2^30911+1 has a factor: 119605419455551563841834379 (ECM curve 389, B1=250000, B2=25000000)
2^30931+1 has a factor: 1612632600033971598883 (ECM curve 79, B1=250000, B2=25000000)
2^30941+1 has a factor: 6904570545676896776397035131 (ECM curve 173, B1=250000, B2=25000000)
2^30941+1 has a factor: 842125849914462691104179 (ECM curve 72, B1=250000, B2=25000000)
2^30949+1 has a factor: 691844779651707379 (ECM curve 4, B1=250000, B2=25000000)
2^30971+1 has a factor: 70988584133311423834721209 (ECM curve 51, B1=250000, B2=25000000)
2^30977+1 has a factor: 55999218230796859867 (ECM curve 45, B1=250000, B2=25000000)
2^30983+1 has a factor: 1120910642269740010644817 (ECM curve 36, B1=250000, B2=25000000)
2^30983+1 has a factor: 1194891090520657056713 (ECM curve 61, B1=250000, B2=25000000)
2^30983+1 has a factor: 151475589627644641 (ECM curve 3, B1=250000, B2=25000000)
[/CODE]

pinhodecarlos 2018-10-20 07:24

I’m holding my range for a week since I’m supporting our friends at SETI.USA on the WCG challenge.

pinhodecarlos 2018-10-24 17:58

24500-25500


[CODE]
2^24509+1 has a factor: 26797559542833811 (ECM curve 1, B1=250000, B2=25000000)
2^24509+1 has a factor: 26797559542833811 (ECM curve 550, B1=250000, B2=25000000)
2^24533+1 has a factor: 2894863821289009873 (ECM curve 7, B1=250000, B2=25000000)
2^24551+1 has a factor: 1208336817408799717197409 (ECM curve 8, B1=250000, B2=25000000)
2^24551+1 has a factor: 48890471181861331193659963 (ECM curve 14, B1=250000, B2=25000000)
2^24551+1 has a factor: 525113083901606204929 (ECM curve 28, B1=250000, B2=25000000)
2^24571+1 has a factor: 466211570336392717642739 (ECM curve 12, B1=250000, B2=25000000)
2^24631+1 has a factor: 17773429471792549703818339 (ECM curve 65, B1=250000, B2=25000000)
2^24659+1 has a factor: 671931499323047842556281 (ECM curve 59, B1=250000, B2=25000000)
2^24691+1 has a factor: 25353368670308820491572378017173491 (ECM curve 400, B1=250000, B2=25000000)
2^24733+1 has a factor: 46168744553355525980338099 (ECM curve 105, B1=250000, B2=25000000)
2^24763+1 has a factor: 5890872034993577 (ECM curve 5, B1=250000, B2=25000000)
2^24767+1 has a factor: 126602987828198606780291 (ECM curve 358, B1=250000, B2=25000000)
2^24767+1 has a factor: 126602987828198606780291 (ECM curve 49, B1=250000, B2=25000000)
2^24793+1 has a factor: 180889058458078202136383707 (ECM curve 86, B1=250000, B2=25000000)
2^24793+1 has a factor: 6986615042857255363937387 (ECM curve 35, B1=250000, B2=25000000)
2^24821+1 has a factor: 2956786439868615955907753 (ECM curve 90, B1=250000, B2=25000000)
2^24847+1 has a factor: 42381098529053649689 (ECM curve 7, B1=250000, B2=25000000)
2^24877+1 has a factor: 36632516057397937902407627251 (ECM curve 302, B1=250000, B2=25000000)
2^24877+1 has a factor: 681084159662746149521 (ECM curve 10, B1=250000, B2=25000000)
2^24877+1 has a factor: 681084159662746149521 (ECM curve 183, B1=250000, B2=25000000)
2^24917+1 has a factor: 21049725597919370836241 (ECM curve 17, B1=250000, B2=25000000)
2^24917+1 has a factor: 21049725597919370836241 (ECM curve 24, B1=250000, B2=25000000)
2^24917+1 has a factor: 646428497909027 (ECM curve 39, B1=250000, B2=25000000)
2^24917+1 has a factor: 646428497909027 (ECM curve 5, B1=250000, B2=25000000)
2^24917+1 has a factor: 652325967318886619722719008137 (ECM curve 276, B1=250000, B2=25000000)
2^24943+1 has a factor: 1347435562899333307 (ECM curve 3, B1=250000, B2=25000000)
2^24953+1 has a factor: 437322164177621915948083 (ECM curve 29, B1=250000, B2=25000000)
2^24977+1 has a factor: 11383554993492641 (ECM curve 1, B1=250000, B2=25000000)
2^24977+1 has a factor: 22510867550389382859923 (ECM curve 1, B1=250000, B2=25000000)
2^24977+1 has a factor: 290398675538456574137512147 (ECM curve 158, B1=250000, B2=25000000)
2^24977+1 has a factor: 55393285958785118466211 (ECM curve 9, B1=250000, B2=25000000)
2^24979+1 has a factor: 10986809760900681009043544953 (ECM curve 206, B1=250000, B2=25000000)
2^25031+1 has a factor: 5929731377757247103689181587 (ECM curve 107, B1=250000, B2=25000000)
2^25057+1 has a factor: 1063592881626649675346933789991107 (ECM curve 188, B1=250000, B2=25000000)
2^25087+1 has a factor: 6535100043369017938551836057 (ECM curve 321, B1=250000, B2=25000000)
2^25097+1 has a factor: 21163232977706224663046809 (ECM curve 231, B1=250000, B2=25000000)
2^25097+1 has a factor: 38470618570424783075891 (ECM curve 4, B1=250000, B2=25000000)
2^25111+1 has a factor: 16816126727551514688707 (ECM curve 18, B1=250000, B2=25000000)
2^25111+1 has a factor: 413707264154384401 (ECM curve 14, B1=250000, B2=25000000)
2^25127+1 has a factor: 6223817007035115525883 (ECM curve 29, B1=250000, B2=25000000)
2^25147+1 has a factor: 1988259831963861516677826091 (ECM curve 153, B1=250000, B2=25000000)
2^25147+1 has a factor: 1988259831963861516677826091 (ECM curve 60, B1=250000, B2=25000000)
2^25147+1 has a factor: 545281377647692979353 (ECM curve 240, B1=250000, B2=25000000)
2^25147+1 has a factor: 545281377647692979353 (ECM curve 56, B1=250000, B2=25000000)
2^25147+1 has a factor: 74846472619123942901102203 (ECM curve 26, B1=250000, B2=25000000)
2^25147+1 has a factor: 74846472619123942901102203 (ECM curve 38, B1=250000, B2=25000000)
2^25163+1 has a factor: 28330515908614135044966227 (ECM curve 114, B1=250000, B2=25000000)
2^25183+1 has a factor: 3446212846301527715145210017851 (ECM curve 216, B1=250000, B2=25000000)
2^25219+1 has a factor: 3902995937050342866347 (ECM curve 8, B1=250000, B2=25000000)
2^25229+1 has a factor: 3867324127268513322670219 (ECM curve 142, B1=250000, B2=25000000)
2^25243+1 has a factor: 332006730590741465387 (ECM curve 4, B1=250000, B2=25000000)
2^25243+1 has a factor: 43059539888548740629899 (ECM curve 2, B1=250000, B2=25000000)
2^25261+1 has a factor: 192442687366658465777 (ECM curve 7, B1=250000, B2=25000000)
2^25307+1 has a factor: 1522507359532596056041 (ECM curve 24, B1=250000, B2=25000000)
2^25309+1 has a factor: 343004287412011924078504643 (ECM curve 70, B1=250000, B2=25000000)
2^25357+1 has a factor: 104863969894610707281492361 (ECM curve 310, B1=250000, B2=25000000)
2^25357+1 has a factor: 191194811605841346747667 (ECM curve 9, B1=250000, B2=25000000)
2^25357+1 has a factor: 644305425688062496290790783691 (ECM curve 85, B1=250000, B2=25000000)
2^25409+1 has a factor: 157426946288271570497 (ECM curve 6, B1=250000, B2=25000000)
2^25409+1 has a factor: 369040328339497275737 (ECM curve 3, B1=250000, B2=25000000)
2^25463+1 has a factor: 6372355641402709002043 (ECM curve 101, B1=250000, B2=25000000)
2^25463+1 has a factor: 6372355641402709002043 (ECM curve 178, B1=250000, B2=25000000)
2^25471+1 has a factor: 14384278291957051 (ECM curve 1, B1=250000, B2=25000000)
2^25471+1 has a factor: 3666847186689120301712921 (ECM curve 9, B1=250000, B2=25000000)
2^25471+1 has a factor: 405802553520011 (ECM curve 3, B1=250000, B2=25000000)
2^25471+1 has a factor: 8999094604678771990891909112587 (ECM curve 346, B1=250000, B2=25000000)

[/CODE]

DukeBG 2018-10-26 16:58

Not sure 100% if it's a relevant information for this thread, but [URL="http://factordb.com/index.php?id=1100000000032220701"]2^1823+1[/URL] and [URL="http://factordb.com/index.php?id=1100000000032220833"]2^1871+1[/URL] have had a P39 and P40 factors added correspondingly yesterday/today by someone. The remaining cofactors are still composite.

GP2 2018-10-26 17:20

[QUOTE=DukeBG;498820]Not sure 100% if it's a relevant information for this thread, but [URL="http://factordb.com/index.php?id=1100000000032220701"]2^1823+1[/URL] and [URL="http://factordb.com/index.php?id=1100000000032220833"]2^1871+1[/URL] have had a P39 and P40 factors added correspondingly yesterday/today by someone. The remaining cofactors are still composite.[/QUOTE]

1823 and 1871 are both prime exponents, so their factors are indeed relevant. I'll update my list later today.

axn 2018-11-07 16:14

[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


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