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

 GP2 2019-06-21 14:11

I am doing the 1300 to 2000 range with ECM up to t=50, using mprime for Stage 1 and GMP-ECM for stage 2.

I found a 48-digit factor today:

2^1301+1 has a factor: 158538524646017900250810607995506380920082613411

This is [I]just[/I] beyond the Cunningham range for 2+ odd. Obviously the factor would have been found long ago if the exponent was the least bit smaller.

It's been [URL="http://factordb.com/index.php?query=2%5E1301%2B1"]added to FactorDB[/URL]. Sigma was 117554418598932.

The 276-digit cofactor is composite.

 LaurV 2019-06-22 08:48

Nice find! Congrats!

 sweety439 2019-06-22 10:22

[QUOTE=GP2;519714]I am doing the 1300 to 2000 range with ECM up to t=50, using mprime for Stage 1 and GMP-ECM for stage 2.

I found a 48-digit factor today:

2^1301+1 has a factor: 158538524646017900250810607995506380920082613411

This is [I]just[/I] beyond the Cunningham range for 2+ odd. Obviously the factor would have been found long ago if the exponent was the least bit smaller.

It's been [URL="http://factordb.com/index.php?query=2%5E1301%2B1"]added to FactorDB[/URL]. Sigma was 117554418598932.

The 276-digit cofactor is composite.[/QUOTE]

You found a factor of Phi_n(2) for n=2602.

Who can give a list (or a text file) of factorization of Phi_n(2) for n<=2^16 like a text file [URL="https://oeis.org/A250197/a250197_1.txt"]factor of Phi_n(2) for n<=1280[/URL]?

(Same as [URL="https://stdkmd.net/nrr/repunit/phin10.htm"]https://stdkmd.net/nrr/repunit/phin10.htm[/URL], but is for Phi_n(2) instead of Phi_n(10))

Also the "First composite factors" (I know the n's are 1207, 1213, ...), "Smallest composite factors", "First blank Φn(2)", "Smallest blank Φn(2)", "Smallest blank Mersenne numbers" (I know this is n=1277), "Smallest blank Wagstaff numbers" (I know this is n=2246=1123*2), and "[URL="https://stdkmd.net/nrr/repunit/prpfactors.htm"]PRP factors list[/URL]", but all are for Phi_n(2) instead of Phi_n(10).

By the way, for the n's such that Phi_n(2) is (probable) prime, see [URL="https://oeis.org/A072226"]OEIS A072226[/URL].

 sweety439 2019-06-22 10:31

[QUOTE=sweety439;519807]You found a factor of Phi_n(2) for n=2602.

Who can give a list (or a text file) of factorization of Phi_n(2) for n<=2^16 like a text file [URL="https://oeis.org/A250197/a250197_1.txt"]factor of Phi_n(2) for n<=1280[/URL]?

(Same as [URL="https://stdkmd.net/nrr/repunit/phin10.htm"]https://stdkmd.net/nrr/repunit/phin10.htm[/URL], but is for Phi_n(2) instead of Phi_n(10))

Also the "First composite factors" (I know the n's are 1207, 1213, ...), "Smallest composite factors", "First blank Φn(2)", "Smallest blank Φn(2)", "Smallest blank Mersenne numbers" (I know this is n=1277), "Smallest blank Wagstaff numbers" (I know this is n=2246=1123*2), and "[URL="https://stdkmd.net/nrr/repunit/prpfactors.htm"]PRP factors list[/URL]", but all are for Phi_n(2) instead of Phi_n(10).

By the way, for the n's such that Phi_n(2) is (probable) prime, see [URL="https://oeis.org/A072226"]OEIS A072226[/URL].[/QUOTE]

Also... (for Phi_n(2) for n<=2^16)

??? of 65536 Φn(2) factorization were finished.
??? of 65536 Φn(2) factorization were cracked.
12 of 16 Fermat factorization were finished.
16 of 16 Fermat factorization were cracked.
??? of 6542 Mersenne factorization were finished.
??? of 6542 Mersenne factorization were cracked.
??? of 3512 Wagstaff factorization were finished.
??? of 3512 Wagstaff factorization were cracked.
??? (probable) prime factors were discovered.
??? composite factors are remaining.
??? factors are unidentified.

I want to know how many..? (like [URL="https://stdkmd.net/nrr/repunit/"]https://stdkmd.net/nrr/repunit/[/URL], but for Phi_n(2) instead of Phi_n(10))

 xilman 2019-06-22 10:57

[QUOTE=sweety439;519807]Who can give a list (or a text file) of factorization of Phi_n(2) for n<=2^16 like a text file?[/QUOTE]I'm almost tempted to do so. Won't happen today though.

 sweety439 2019-06-23 09:35

[QUOTE=xilman;519810]I'm almost tempted to do so. Won't happen today though.[/QUOTE]

Thanks!!!

 sweety439 2019-06-23 14:05

It seems that small [URL="https://stdkmd.net/nrr/repunit/phin10.htm"]factors of Phi_n(10)[/URL] are searched for all n around 100000 and 200000, but small factors of Phi_n(2) are only searched by prime n and the n's which are power of 2, I know this project is searching this for n's which are twice an odd prime, bur how about other n? Is there anyone searching small factors of Phi_n(2) for all n around 100000 and 200000?

 GP2 2019-06-24 04:52

The "[URL="https://oeis.org/A250197/a250197_2.txt"]factors of Phi_n(2) for n<=1280[/URL]" file is subject to updates as new factors are found.

Because of the way OEIS handles files, every time the contents are updated, the link changes. The latest link is now _2.txt, which differs from _1.txt by having additional factors for exponents 991, 1213, 1219, 1261.

 sweety439 2019-06-24 21:07

[QUOTE=GP2;519951]The "[URL="https://oeis.org/A250197/a250197_2.txt"]factors of Phi_n(2) for n<=1280[/URL]" file is subject to updates as new factors are found.

Because of the way OEIS handles files, every time the contents are updated, the link changes. The latest link is now _2.txt, which differs from _1.txt by having additional factors for exponents 991, 1213, 1219, 1261.[/QUOTE]

Well, can you extend this list to n=2000 or above?

 GP2 2019-06-25 03:21

[QUOTE=sweety439;520008]Well, can you extend this list to n=2000 or above?[/QUOTE]

The recent factors for those four exponents were readily available from the Cunningham tables.

If you want exponents beyond the Cunningham range, you could probably gather the data from FactorDB.com

 sweety439 2019-06-25 16:56

[QUOTE=GP2;520018]The recent factors for those four exponents were readily available from the Cunningham tables.

If you want exponents beyond the Cunningham range, you could probably gather the data from FactorDB.com[/QUOTE]

However, you cannot enter "Phi_n(2)" in factordb, since factordb has no "cyclotomic polynomial" function, you can only enter "2^n-1" (I know that 2^n-1 = prod{d|n}Phi_d(2))

 GP2 2019-06-28 15:00

[URL="https://www.mersenne.ca/exponent/1073741827"]M1,073,741,827[/URL] has a factor: 16084529043983099051873383

This exponent is relevant to the (trivial) "[URL="http://mprime.s3-website.us-west-1.amazonaws.com/new_mersenne_conjecture.html"]New Mersenne Conjecture[/URL]"

 sweety439 2019-06-29 00:02

[QUOTE=GP2;520259][URL="https://www.mersenne.ca/exponent/1073741827"]M1,073,741,827[/URL] has a factor: 16084529043983099051873383

This exponent is relevant to the (trivial) "[URL="http://mprime.s3-website.us-west-1.amazonaws.com/new_mersenne_conjecture.html"]New Mersenne Conjecture[/URL]"[/QUOTE]

M1,073,741,827 is Phi(2^30+3, 2)

Conjectures:

* Phi(2^n-1,2) is composite for all n>7 (it is prime for n = 2, 3, 4, 5, 7)
* Phi(2^n+1,2) is composite for all n>7 (it is prime for all n <= 7)
* Phi(2^n-3,2) is composite for all n>6 (it is prime for n = 3, 4, 6)
* Phi(2^n+3,2) is composite for all n>4 (it is prime for n = 1, 2, 4)

* Phi(2*(2^n-1),2) is composite for all n>7 (it is prime for all n <= 7)
* Phi(2*(2^n+1),2) is composite for all n>4 (it is prime for n = 1, 2, 4)
* Phi(2*(2^n-3),2) is composite for all n>6 (it is prime for n = 2, 3, 4, 6)
* Phi(2*(2^n+3),2) is composite for all n>4 (it is prime for n = 1, 2, 3, 4)

* There are no odd n>345 such that both Phi(n,2) and Phi(2*n,2) are primes (there are both primes for n = 3, 5, 7, 13, 15, 17, 19, 31, 49, 61, 85, 127, 345, only consider odd n)
* There are no odd n>345 such that both Phi(n,2)/gcd(Phi(n,2),n) and Phi(2*n,2)/gcd(Phi(2*n,2),n) are primes (there are both primes for n = 5, 7, 9, 13, 15, 17, 19, 21, 27, 31, 49, 61, 85, 127, 345, only consider odd n)

Related to the New Mersenne Conjecture

 sweety439 2019-06-29 00:11

The conjecture that there are only 5 Fermat primes is that there are no n>5 such that Phi(2^n,2) is prime, I conjectured that there are no n>7 such that Phi(2^n-1,2) is prime, no n>7 such that Phi(2^n+1,2) is prime, no n>7 such that Phi(2*(2^n-1),2) is prime, and no n>4 such that Phi(2*(2^n+1),2) is prime.

More generally, for every (positive or negative or zero, odd or even) integer k, there are only finitely many n such that 2^n+k is in [URL="https://oeis.org/A072226"]OEIS A072226[/URL], i.e. there are only finitely many n such that Phi(2^n+k,2) is prime.

[CODE]
k conjectured full list of such n
-16 5,
-15 5, 6,
-14 4,
-13 4, 5,
-12 4,
-11 4, 11,
-10 4, 5,
-9 4,
-8 4, 5, 6, 7,
-7 4,
-6 3, 4, 5, 7,
-5 3, 5, 9,
-4 3, 4,
-3 3, 4, 6,
-2 2, 3, 4, 5, 6, 7, 8,
-1 2, 3, 4, 5, 7,
0 1, 2, 3, 4, 5,
1 1, 2, 3, 4, 5, 6, 7,
2 1, 2, 3, 5,
3 1, 2, 4,
4 1, 2, 3,
5 1, 2, 3, 6, 7, 8,
6 1, 2, 3, 4, 5,
7 1, 3,
8 1, 2, 3, 4, 5,
9 2, 3, 9,
10 1, 2, 4, 5,
11 1, 2, 3, 4,
12 1, 2,
13 1, 2, 6,
14 1, 3, 4, 5, 6,
15 1, 2, 4,
16 3, 4, 6,
[/CODE]

 axn 2019-07-01 03:55

[CODE]ECM found a factor in curve #8, stage #2
Sigma=5999343673417650, B1=50000, B2=5000000.
2^114743+1 has a factor: 363690536981293584763 (ECM curve 8, B1=50000, B2=5000000)[/CODE]
W114743 = 565224019 · 581747011 · 601253321 · 810315067 · 69667542321371 · 7485151305966881 · 13863811976194993 · 363690536981293584763 · PRP34439

 paulunderwood 2019-07-01 05:35

[QUOTE=axn;520425][CODE]ECM found a factor in curve #8, stage #2
Sigma=5999343673417650, B1=50000, B2=5000000.
2^114743+1 has a factor: 363690536981293584763 (ECM curve 8, B1=50000, B2=5000000)[/CODE]
W114743 = 565224019 · 581747011 · 601253321 · 810315067 · 69667542321371 · 7485151305966881 · 13863811976194993 · 363690536981293584763 · PRP34439[/QUOTE]

Congrats :toot:

[CODE]time echo 'print((2^114743+1)/3/565224019/581747011/601253321/810315067/69667542321371/7485151305966881/13863811976194993/363690536981293584763)' | gp -q | ./bpsw-2 - 1 2 114743 1
Testing (2*x)^((n + 1)/2) == -2 (mod n, x^2 - 9*x + 1)...
Likely prime!

real 0m8.926s
user 0m8.980s
sys 0m0.000s

[/CODE]

Well within reach of a Primo proof. Edit: A hard proof for Primo -- I was thinking base 2!

 axn 2019-07-01 05:45

[QUOTE=paulunderwood;520432]Well within reach of a Primo proof.[/QUOTE]
This would go as #2 on [url]http://www.ellipsa.eu/public/primo/top20.html#PrimoRecord[/url] (if it were to be attempted).

How many core years do you estimate to prove this one?

EDIT:- Just missed paul's edit. The question still stands.

 paulunderwood 2019-07-01 06:00

[QUOTE=axn;520434]This would go as #2 on [url]http://www.ellipsa.eu/public/primo/top20.html#PrimoRecord[/url] (if it were to be attempted).

How many core years do you estimate to prove this one?

EDIT:- Just missed paul's edit. The question still stands.[/QUOTE]

I took some 14 months on a 48 core AMD 6174 @ 2.2GHz for similarly sized numbers -- but now Primo is quicker. 14 months is an upper bound -- say 1 year on such a machine. Much quicker on a 64 core AMD 7 series EPYC.

 GP2 2019-07-01 06:46

Congratulations on the PRP for 114743

There are smaller Wagstaff exponents with uncertified PRPs: 31601, 32369, 32377, 35677, 35851, 41269, 53759, 62581, 70921, 80819, 83423, 85517, 91159, 102299

There are also these uncertified Wagstaff prime exponents: 95369, 117239. Also the prime for 42737 has an old-fashioned certificate (that maybe can be verified with the Maple program, I'm not sure) rather than a Primo certificate.

A lot of work if anyone wanted to tackle it.

PS,
Also Mersenne PRPs with exponents 78737, 82939, 84211, 86137, 86371, 87691, 106391

 sweety439 2019-07-01 13:04

Well, can Phi(2^n-1,2) or Phi(2^n+1,2) be prime for any n>7?

 GP2 2019-07-03 10:39

W5261 has a 48-digit factor: 726665169300701944892064737622954607252115216339

The [URL="http://factordb.com/index.php?id=1100000001321603291"]cofactor is a probable prime[/URL].

 axn 2019-07-03 11:18

[QUOTE=GP2;520639]W5261 has a 48-digit factor: 726665169300701944892064737622954607252115216339

The [URL="http://factordb.com/index.php?id=1100000001321603291"]cofactor is a probable prime[/URL].[/QUOTE]

:w00t: Now [B]there's[/B] an easily provable PRP

 GP2 2019-07-03 13:25

[QUOTE=axn;520645]:w00t: Now [B]there's[/B] an easily provable PRP[/QUOTE]

It was an extremely lucky hit. I was only doing t=40, yet it found a 48-digit factor after less than 700 curves. The recommended curves for GMP-ECM version 7 are 2753 for t=40, 5208 for t=45, and 8704 for t=50.

 Dylan14 2019-07-07 22:15

[QUOTE=GP2;520442]Congratulations on the PRP for 114743

There are smaller Wagstaff exponents with uncertified PRPs: 31601, 32369, 32377, 35677, 35851, 41269, 53759, 62581, 70921, 80819, 83423, 85517, 91159, 102299
[/QUOTE]

I have done the Primo certification for the cofactor of W31601: [url]http://factordb.com/index.php?id=1100000001188126321[/url]

 paulunderwood 2019-07-07 23:00

[QUOTE=Dylan14;520971]I have done the Primo certification for the cofactor of W31601: [url]http://factordb.com/index.php?id=1100000001188126321[/url][/QUOTE]

How long did it take? What about doing the next few in the list!

 Dylan14 2019-07-07 23:35

[QUOTE=paulunderwood;520975]How long did it take? What about doing the next few in the list![/QUOTE]

It took 476222s or about 132.3 hours to do on an Intel i5-6400. I’ll tackle the next one after I finish doing the factorization of 7*2^705+1.

 axn 2019-07-11 15:05

116k-120k

[CODE]2^116027+1 = 1094948183730961067
2^116041+1 = 875417328300133222062491
2^116107+1 = 33626844482729187593
2^116131+1 = 739645302376182091
2^116159+1 = 179145631566848627
2^116167+1 = 41899885901495539086683
2^116201+1 = 2407642862916145633
2^116257+1 = 138257604673229579
2^116269+1 = 19150533962363051561
2^116269+1 = 720083625776105056559113
2^116329+1 = 12216621437032852097
2^116341+1 = 10062744754478490220067
2^116381+1 = 127062909322205450715203
2^116387+1 = 205592347123322633
2^116443+1 = 3114110896328363999633
2^116447+1 = 111184444974432443
2^116507+1 = 1591460436684305286377
2^116537+1 = 75228214722812123929163
2^116657+1 = 1818929739775860043
2^116687+1 = 295829766978263867
2^116747+1 = 374622899681277683
2^116791+1 = 62613492812492702137
2^116797+1 = 1081653129441765543731
2^116819+1 = 3366170498848051547
2^116819+1 = 5106576796786142819
2^116827+1 = 55771861387027615307
2^116833+1 = 468588970251220033
2^116849+1 = 279134565031287987169
2^116911+1 = 103678486688819575699
2^116911+1 = 2249530050218151929
2^116927+1 = 30752583258150148123
2^116933+1 = 394113607716969035840921
2^116959+1 = 2083333502281749852097
2^116969+1 = 8582767342918392361
2^117041+1 = 3572912173607115501737
2^117071+1 = 1688736755086524313
2^117163+1 = 5000015678314113109763779
2^117191+1 = 3653937140571010802441521
2^117209+1 = 40631584084964272450660963
2^117223+1 = 1805225763028126814377
2^117251+1 = 4170691322154920027
2^117269+1 = 55133324588505798121
2^117269+1 = 5704547556095894792651
2^117319+1 = 31987648662520046153113777
2^117329+1 = 137372153092377817
2^117331+1 = 132682310882544744883
2^117353+1 = 320759980930197529354649
2^117361+1 = 309908197417095938483
2^117373+1 = 329429988641312969
2^117413+1 = 32955651356054043707
2^117427+1 = 2003014686302828025497
2^117511+1 = 332288325402446836963
2^117511+1 = 6674162418797361113
2^117541+1 = 887345979788572702609
2^117671+1 = 206536857424011203
2^117703+1 = 213676532369079817
2^117731+1 = 75432528690664859975803
2^117751+1 = 3038575121094904529
2^117773+1 = 7766103721887637105769
2^117779+1 = 4231200140792321611
2^117787+1 = 13080610077166964659
2^117833+1 = 56942952127191081180397699
2^117841+1 = 221156122802321317379
2^117841+1 = 287862923757807787
2^117881+1 = 2328991366385630539
2^117881+1 = 25194006846584492840841881
2^117899+1 = 13015499294608066378901079137
2^117911+1 = 53492712431598453931
2^117973+1 = 4023022306412156923
2^117979+1 = 1075710170288319043
2^117979+1 = 166315609681197959977087081
2^117991+1 = 47194043904265092217
2^118037+1 = 13896405384590865601
2^118043+1 = 2737140250271512931
2^118081+1 = 33529997052604238980291
2^118093+1 = 329186739812397017690233
2^118127+1 = 1345536558742490507
2^118147+1 = 676354058229929539
2^118211+1 = 13822173369178444847323
2^118213+1 = 60261385225871872907
2^118249+1 = 248640562949083849
2^118277+1 = 420988692530926441
2^118409+1 = 788201449342169179
2^118411+1 = 33209953725170651502937
2^118457+1 = 100403275081323002128409
2^118571+1 = 24775852199867639549199717419
2^118619+1 = 21671515740250258601
2^118669+1 = 608865230673060783725763888313
2^118687+1 = 173547405203339249
2^118709+1 = 91405902970136389321
2^118739+1 = 4656171238367965139
2^118799+1 = 179478376173077813267
2^118843+1 = 190133356384827784339
2^118901+1 = 2271967370902372706267
2^118907+1 = 266012175155350846656700249
2^118973+1 = 43549919260451553335857
2^119033+1 = 373629052645234003
2^119047+1 = 1396308816561565112177
2^119057+1 = 21486798664432140043
2^119069+1 = 141784855234764587599406251
2^119069+1 = 221721729748451909371
2^119101+1 = 20097879346272135085107611
2^119159+1 = 20077616943792160494160067654230691
2^119183+1 = 359198876945936529776250707
2^119191+1 = 8849852009221809357001
2^119227+1 = 5768395206976039241
2^119243+1 = 583144619442294945932497
2^119299+1 = 8373217461424855163353
2^119321+1 = 1211599729053906402673
2^119389+1 = 43768762857937907819
2^119447+1 = 23089647113601483083
2^119513+1 = 34635552772941576423937
2^119549+1 = 80627231877070169
2^119551+1 = 65849176302934384980883
2^119569+1 = 1694762095697562740969
2^119611+1 = 3950578164333541369
2^119671+1 = 12792891279373416923
2^119677+1 = 141030535859196289
2^119677+1 = 280653631721040307
2^119689+1 = 265185385790827550541403
2^119689+1 = 930524117144940089
2^119737+1 = 12677551905220734593
2^119737+1 = 271976908307887259
2^119737+1 = 2762925719490783233051557961
2^119747+1 = 185763013501621418657
2^119747+1 = 22441276635930409578611
2^119771+1 = 13520193560065116593
2^119773+1 = 478383994637331292403
2^119809+1 = 5140221356489006546747
2^119813+1 = 629737739428024219
2^119839+1 = 22340608462138988994257
2^119891+1 = 536348139222587514817
2^119971+1 = 23586149201893829699
2^119971+1 = 334101038086380794210483
2^119981+1 = 29211163456925200704553
2^119981+1 = 3320252131980218843[/CODE]
114k-116k is being worked on on a slower 'puter

 axn 2019-07-17 15:23

120k-125k

[CODE]2^120017+1 = 39071791252947189017
2^120067+1 = 15983024328677785993
2^120079+1 = 6845714964170128939
2^120079+1 = 79735112578475952331
2^120091+1 = 4560192026327877113
2^120121+1 = 3329137765337185043010331
2^120163+1 = 3746432206888058082713
2^120167+1 = 412318403576107204593779
2^120181+1 = 217160370505065521
2^120199+1 = 2213378176385917217092291
2^120199+1 = 3858499736845275715690001
2^120277+1 = 1245766777845727513
2^120293+1 = 1083950572768438552643
2^120299+1 = 134720134464355922227
2^120319+1 = 17982344164275868483
2^120331+1 = 2965410264358240853353
2^120397+1 = 5571107416909689116405246803
2^120401+1 = 169348138478806841653793
2^120511+1 = 26055186938975045301233233
2^120551+1 = 81349070127459649
2^120569+1 = 260942838791334043
2^120619+1 = 4299835901357861897083
2^120623+1 = 1107110847220040059
2^120623+1 = 117663335121127441
2^120671+1 = 224262498752590931
2^120677+1 = 26696521478492684747
2^120689+1 = 1180225456101339371
2^120691+1 = 87378383989222342417
2^120709+1 = 252840731214797881
2^120713+1 = 53933721700181677187123
2^120713+1 = 651282378973209517867
2^120739+1 = 44181797757191946887449
2^120767+1 = 13837647510757656403
2^120767+1 = 5848308331971222851
2^120779+1 = 255785654792484169
2^120779+1 = 29103964035990653291
2^120811+1 = 60845463996880937603
2^120851+1 = 1433092016799833165089
2^120877+1 = 261667141414722486259
2^120889+1 = 4952116122519865729
2^120907+1 = 5325573807272687083
2^120929+1 = 12055994725031690734287843979
2^120929+1 = 2416978350479852507
2^120929+1 = 82478601287117450883161
2^120941+1 = 565236633048027209803
2^120941+1 = 71939119934628226393123
2^120947+1 = 5700742623890364303552713
2^120977+1 = 1048606264957915268248531
2^121001+1 = 13972679292375693833
2^121001+1 = 3624038016747135773282291
2^121013+1 = 163954660356148877080427
2^121081+1 = 4451816223089256713
2^121081+1 = 741944793257913359845067
2^121139+1 = 617928598904413561
2^121157+1 = 3936270279370822861987
2^121169+1 = 44765272162840196147
2^121181+1 = 6558521264321548427
2^121189+1 = 638877403433201450657
2^121229+1 = 3195685569749564621827
2^121267+1 = 1521907641774009863938403
2^121271+1 = 1124216602994929206307
2^121283+1 = 1946167783555619371987
2^121283+1 = 3438700117191194729
2^121333+1 = 51568528891031573208779
2^121343+1 = 26331988270490965483
2^121379+1 = 12296426529426281267
2^121403+1 = 12388495725094498282650323
2^121447+1 = 6034204864641947559953
2^121487+1 = 10256245172773264437775338913
2^121493+1 = 383780071653380166883
2^121501+1 = 50782766985321694553731
2^121523+1 = 12612705932592106239427
2^121523+1 = 3744662291963733987290011
2^121547+1 = 1365917940095463449
2^121571+1 = 244070468504740070233
2^121577+1 = 75711182320655009
2^121591+1 = 6248582637105021620260859323
2^121607+1 = 497252638229898233
2^121609+1 = 111998316776585100163
2^121637+1 = 172542708522574535002298741185465054896721
2^121661+1 = 535272823375092377483
2^121697+1 = 103879866058868428171
2^121763+1 = 579284672367160607297
2^121843+1 = 385942423874258759539
2^121883+1 = 15219318721364049663460661254609
2^121909+1 = 2147224090110499112683
2^121909+1 = 380521287390164879169492961
2^121993+1 = 2482267850659025183250859507
2^121997+1 = 547652447522824206481033
2^122033+1 = 13295973934566202272251
2^122039+1 = 1875751493205301286857
2^122081+1 = 90671880070452569627
2^122149+1 = 45716890977294117121
2^122167+1 = 1424549171933711266819
2^122207+1 = 31962576674946109889
2^122231+1 = 18291091349323833601572397387
2^122263+1 = 24327115811784029401
2^122263+1 = 98994582267383281
2^122273+1 = 102504968015533236563
2^122279+1 = 11523494771756083093889
2^122323+1 = 20506436259404376233
2^122323+1 = 31096848713829790249
2^122363+1 = 3151569707162213459
2^122399+1 = 175018069577117483513
2^122399+1 = 42798575027701262756923
2^122399+1 = 859307981040829039871080427
2^122453+1 = 175018333848423075323
2^122477+1 = 81056019784997603
2^122497+1 = 1967734894337843107
2^122503+1 = 233398034421571639931
2^122509+1 = 164182377375735497
2^122527+1 = 80485862463052153
2^122527+1 = 887619447285557812152165409
2^122579+1 = 2946565906928898920517569
2^122597+1 = 6020473364341837812881
2^122651+1 = 52371757520436335379659
2^122693+1 = 7112574506762220889
2^122701+1 = 115582494910435019
2^122743+1 = 140836708381005976771
2^122753+1 = 20725045499649761414251
2^122819+1 = 21393602588051783135329
2^122849+1 = 23893176794527080544771507
2^123017+1 = 111118002986292793
2^123031+1 = 1400095406682076499
2^123031+1 = 1909319568202697249
2^123059+1 = 125919610809973155233
2^123059+1 = 471262112428028147
2^123121+1 = 3226221698211264144787
2^123127+1 = 7930870541085943036321899211
2^123169+1 = 285513437807029273
2^123191+1 = 32859580075237686523
2^123229+1 = 345467060810506009
2^123269+1 = 152825375598579179
2^123269+1 = 170191612675323611
2^123269+1 = 86666253241166447791577
2^123289+1 = 201452966985911347523
2^123289+1 = 3905265455416896713
2^123289+1 = 729153586235104728544361
2^123311+1 = 823895633369705779
2^123323+1 = 6989359599899046233
2^123373+1 = 19490478928354584979001
2^123379+1 = 2674623067040480757059
2^123407+1 = 151659085914896514667
2^123427+1 = 41702311407108949894793
2^123439+1 = 22356140321377503951553
2^123457+1 = 301183871038130099
2^123517+1 = 22475325310035701436667
2^123593+1 = 4368630713238355307
2^123637+1 = 625201599412133123
2^123653+1 = 248657993660342852774753
2^123707+1 = 817809063261943369251937
2^123803+1 = 15186695433777024483583921
2^123817+1 = 143487431508597289
2^123829+1 = 763968061159561385876633
2^123887+1 = 4274038081285071299
2^123911+1 = 14406550018015417697
2^123953+1 = 11441963493410219914699
2^123953+1 = 8466140130495607559833
2^124021+1 = 3237507914864886624361
2^124067+1 = 657078625778954083
2^124087+1 = 161013434916056369
2^124133+1 = 5072828094915000595481
2^124193+1 = 219541474269980636334563
2^124199+1 = 18596467835523415477871971
2^124249+1 = 173858299304886192101297
2^124303+1 = 35710891007093245113683
2^124303+1 = 407519984834066324713
2^124303+1 = 751593266218284132641
2^124337+1 = 14566581597435247268923
2^124339+1 = 96220904072049534160489
2^124429+1 = 3056167505697890019083
2^124447+1 = 33374452821572406563
2^124541+1 = 1034944733005775086549921
2^124601+1 = 11129786568398675996699
2^124601+1 = 386238465708100187131
2^124643+1 = 126825656591742375217
2^124643+1 = 1882431603335293417249
2^124693+1 = 13615129719355117297
2^124703+1 = 481499969777245667
2^124717+1 = 6987832051499927362856347
2^124721+1 = 13871977244770208507
2^124777+1 = 4883441354464665313
2^124793+1 = 51699052562325677127720833
2^124823+1 = 45410756838701026374368771
2^124909+1 = 74328289301748395737
2^124909+1 = 934861200933283121
2^124987+1 = 17838917614651494631147
2^124987+1 = 311397204222338401[/CODE]

 Dylan14 2019-07-18 12:29

I have done the Primo certification on the cofactor of W32369: [url]http://factordb.com/index.php?id=1100000000026866864[/url] (still processing at the time of post). This cert took 645490s or about 179.3 hours to do.
Now I will take on W32377.

 paulunderwood 2019-07-18 12:33

[QUOTE=Dylan14;521850]I have done the Primo certification on the cofactor of W32369: [url]http://factordb.com/index.php?id=1100000000026866864[/url] (still processing at the time of post). This cert took 645490s or about 179.3 hours to do.
Now I will take on W32377.[/QUOTE]

:tu:

 GP2 2019-07-19 00:32

Someone found a 53-digit factor for W5237: 28101629210906800044136226409280228946441472707288921

I found out by checking FactorDB.

I'm ECM testing the 5k Wagstaff range myself right now, but only up to t=40. I tested this very same exponent a few weeks ago, but obviously found nothing.

Does anyone know who found it?

Obviously, this is also a factor of M10474. Maybe Ryan Propper is checking composite Mersenne exponents too now?

 axn 2019-07-24 16:59

125k-130k

[CODE]2^125017+1 = 14971644694903872043
2^125029+1 = 9042454211011037563
2^125093+1 = 167613452471535857
2^125113+1 = 15479509894438605881201201
2^125113+1 = 3140890065442810864845174379
2^125131+1 = 1319047591062538993509851
2^125149+1 = 3442045077314090048233
2^125197+1 = 152244519528027645122737
2^125207+1 = 1125319824377829299
2^125329+1 = 373794273972413323
2^125353+1 = 83372834431711211
2^125383+1 = 3730493729527095787
2^125387+1 = 1813121548142943019
2^125527+1 = 240922615781683284953027
2^125591+1 = 1386700299039738497
2^125651+1 = 27076150915182507899
2^125659+1 = 22452642881256916098649
2^125669+1 = 23745871740976910066819
2^125687+1 = 40698051999038540737
2^125737+1 = 115246885072123705291
2^125753+1 = 1751641466786083493365993
2^125789+1 = 1638472472142985057
2^125803+1 = 344667603909637553
2^125821+1 = 79148863605616627
2^125927+1 = 116227734985621243
2^125927+1 = 334015377635458546053017
2^126013+1 = 1898389691244977822874113
2^126019+1 = 190810412334714041
2^126127+1 = 121003976698202243
2^126131+1 = 25495095449212362987161
2^126131+1 = 671905790418264419
2^126151+1 = 21601783675322682127403
2^126173+1 = 2249306078942271619
2^126173+1 = 54642667278005657295443
2^126199+1 = 170152974856814358195323
2^126211+1 = 97774039466600417
2^126223+1 = 269462091395378478329
2^126241+1 = 112818075188897649775869019
2^126241+1 = 6755268795903294493819
2^126337+1 = 1240459878832430601529
2^126337+1 = 402597625017339992905619
2^126359+1 = 233300637170999615311681
2^126397+1 = 2345122699532146379
2^126397+1 = 843045056861513867731
2^126457+1 = 1942854177940834889
2^126457+1 = 5984249387700482057
2^126461+1 = 11197134760664602083264571
2^126481+1 = 110129090651718038593859
2^126487+1 = 5897076513785013041
2^126493+1 = 49601884685843728217162177
2^126499+1 = 3013273628544237713
2^126601+1 = 4393544744710185923
2^126719+1 = 1640716259517190444289
2^126739+1 = 20792550957573573259
2^126823+1 = 34694244457436191843
2^126839+1 = 2829071052920699763161
2^126851+1 = 6394723606264934539
2^126857+1 = 33194837096489987603593
2^126923+1 = 18163701112529686348681
2^126943+1 = 19580317626974647893349067
2^126943+1 = 890592460492104497
2^126943+1 = 9353263916882039436195659
2^126949+1 = 324362955098838298986260849
2^126989+1 = 10730350075035972565207993
2^127081+1 = 7020944612166343427
2^127139+1 = 375959580922500329
2^127163+1 = 236070341753994499
2^127207+1 = 681440066054330983217
2^127271+1 = 15884625181432318860851
2^127271+1 = 51755522283951422059
2^127291+1 = 2108238407552023552455333881
2^127297+1 = 43637188527237313081
2^127399+1 = 11148155280213363089
2^127447+1 = 11043393572403295084321
2^127453+1 = 98014392029705805169
2^127493+1 = 10173828131851964857
2^127601+1 = 146457766486170673
2^127609+1 = 2687345973261134341721
2^127649+1 = 16758680684469367979
2^127649+1 = 5215730515832556711209
2^127657+1 = 871352029999595393
2^127679+1 = 3824818260593741259514793
2^127691+1 = 683781327251558553548611
2^127703+1 = 214727693752281463692569
2^127703+1 = 579880304638668627211
2^127711+1 = 81809133295495853459
2^127837+1 = 102885115700633412217
2^127873+1 = 2885773793293961803
2^127973+1 = 31944703787193380917912124851
2^128021+1 = 177708829776977507
2^128021+1 = 90517193759511729342529
2^128033+1 = 323295041023094976256777
2^128047+1 = 6094128580357064157089
2^128111+1 = 1126509539884596726427
2^128111+1 = 175139465806752258881
2^128119+1 = 42398365715195757386051
2^128153+1 = 58706161022053292327273
2^128213+1 = 7679307045095460809
2^128221+1 = 17506402830785945313649
2^128237+1 = 16976639203187355521
2^128257+1 = 250598955640447313
2^128273+1 = 128492721788654491
2^128341+1 = 151235123994252018366803
2^128393+1 = 584071826209314227
2^128411+1 = 3233920836269221061779
2^128437+1 = 73287933506367323
2^128483+1 = 45520650205898122838603
2^128549+1 = 666753466420573163
2^128603+1 = 649569029937244190438507
2^128629+1 = 23591304531410270419
2^128677+1 = 53265188621798380833243619
2^128717+1 = 3861189570765688363
2^128767+1 = 99447767659981700809
2^128819+1 = 7274177268232578883
2^128831+1 = 934814720998387780656689
2^128833+1 = 2023562994393928639775587
2^128857+1 = 534422133329550601
2^128861+1 = 7116416641053432856411
2^128879+1 = 1524542053188875107
2^128959+1 = 1281960464613804587
2^128971+1 = 13678085347809362153
2^128983+1 = 4543810460864266129
2^128987+1 = 66328113834055647449353
2^129001+1 = 288174956589394158257
2^129001+1 = 4630827335194647597011
2^129011+1 = 93569908218470532833
2^129119+1 = 3649462360172956813417
2^129127+1 = 1822162328959530737
2^129229+1 = 2284172853118684284923
2^129229+1 = 37277840277235942570819
2^129281+1 = 173288611868784654769
2^129341+1 = 297405242234463851
2^129347+1 = 679252926192598787
2^129361+1 = 21683927489395259741731697
2^129361+1 = 3824730915970250971
2^129379+1 = 496565462150014787
2^129401+1 = 23636084769001985977043
2^129401+1 = 283436366941844539
2^129439+1 = 103681874180459353
2^129457+1 = 132277708236604018603363
2^129457+1 = 21144963829865039148697
2^129499+1 = 33537348828088214297
2^129527+1 = 46931228353387044523
2^129533+1 = 218060672005056010409057
2^129539+1 = 4804983326346506951833
2^129589+1 = 6600999827370790575330449
2^129629+1 = 7432013670360695681948611
2^129671+1 = 3067040910038281060691
2^129707+1 = 17581755482484132693931
2^129757+1 = 116163393187066213987
2^129757+1 = 27147464687336514477213713
2^129769+1 = 37020430367674066771
2^129803+1 = 111498773000558873
2^129841+1 = 391451567183253947
2^129887+1 = 3204608126250631169
2^129887+1 = 43450601640322297072348841
2^129937+1 = 3258419832778963387
2^129937+1 = 370775520798040223083[/CODE]

 axn 2019-07-25 05:45

114k-116k

[CODE]2^114001+1 = 3892323188051837770004539
2^114041+1 = 6363688797878321401
2^114043+1 = 658158286513631661021377
2^114073+1 = 2706634478134824473
2^114083+1 = 15768479951686599329
2^114113+1 = 18644211061708479631627
2^114157+1 = 103432527552452049769283
2^114197+1 = 45621761073983313283
2^114203+1 = 152233530752812627
2^114203+1 = 3240093028945216097321
2^114217+1 = 59782514212033830403
2^114221+1 = 265229897643698093177834249
2^114319+1 = 29049272401134955771
2^114329+1 = 4707060024919257001
2^114377+1 = 25848050414189112073153753
2^114377+1 = 278570668680762803
2^114451+1 = 1583920201353597905561
2^114547+1 = 424066148804874760088603
2^114571+1 = 314943009485847233
2^114577+1 = 33625644024221957377
2^114613+1 = 30530259329846165089
2^114613+1 = 862272668036945711443
2^114643+1 = 1442874130724362067
2^114649+1 = 241161905458087026323
2^114649+1 = 2605035157311700667
2^114649+1 = 395848842680911544609
2^114713+1 = 360027441586007447299
2^114743+1 = 363690536981293584763
2^114749+1 = 1265388202166388160481
2^114749+1 = 130919486141694227
2^114757+1 = 33192087123915445922199164947
2^114761+1 = 5401133821288035225762922777
2^114781+1 = 3401887084058386681
2^114809+1 = 96745627886942603
2^114827+1 = 25483739181396706163
2^114859+1 = 12470837542371415819
2^114901+1 = 54118579100939748739
2^114913+1 = 80421055366593539325163
2^114941+1 = 88187558747609793426121
2^114973+1 = 501503128223767000651
2^115021+1 = 115354096227432969780821032409
2^115021+1 = 222880163443760960323
2^115057+1 = 76760770736385312419
2^115067+1 = 23586099640602214554701099
2^115067+1 = 3444831106745188243
2^115123+1 = 410274899547584417
2^115123+1 = 7665239433016124977
2^115183+1 = 8111279104509642988067
2^115211+1 = 233502030399622769
2^115249+1 = 12965127953995654219
2^115301+1 = 2605990492966411417
2^115319+1 = 3039461847157658369510473
2^115321+1 = 28333251213787134859
2^115327+1 = 99568019717036754612667
2^115337+1 = 121484084555172179
2^115553+1 = 15735702654770252129
2^115571+1 = 451076321170275296137
2^115603+1 = 10865556222813793723769
2^115613+1 = 52848650564359296581574427
2^115679+1 = 3718019199240222761603
2^115693+1 = 96393477300662732363
2^115751+1 = 434679871411099790146387
2^115757+1 = 472166627250288650681
2^115793+1 = 1023770269397259767633
2^115849+1 = 137943819921252937
2^115859+1 = 65497081034000666046697
2^115861+1 = 41514828689662694713769
2^115933+1 = 8357371763220087563
2^115963+1 = 1087222604151145273451371
2^115963+1 = 65082919615267165994586041
2^115979+1 = 151816508446374379
2^115981+1 = 449734111911913896110125921
2^115981+1 = 7835635038499454375801[/CODE]

 Dylan14 2019-07-26 11:37

I have done the Primo certification for W32377: [url]http://factordb.com/index.php?id=1100000001189041877[/url]. This took 647851 s or ~ 180 hours to do.

 axn 2019-07-27 11:06

130k-132k

[CODE]2^130003+1 = 8552971432487761052297
2^130069+1 = 291505231566707491
2^130183+1 = 6202030351070230051
2^130337+1 = 30571110575373807497
2^130337+1 = 3558810310997090353
2^130399+1 = 26776404676366266149480971
2^130411+1 = 21276440002081818445423979
2^130423+1 = 3449429807331381775289
2^130439+1 = 2011201776992594448115739
2^130469+1 = 2524909325613510305463611
2^130469+1 = 598151672007037279180697
2^130477+1 = 11678533436683014721
2^130489+1 = 121138702596163469259811
2^130517+1 = 2897970474089075393
2^130547+1 = 508006319976349508311993
2^130579+1 = 1523045453621444959350779
2^130621+1 = 9128619307406165799425729
2^130657+1 = 185880109834595640449
2^130687+1 = 2465324010508352852846723
2^130687+1 = 6383007919297667849
2^130693+1 = 1266101263818972419
2^130729+1 = 36675899698773063046067
2^130807+1 = 1225853296424814694577
2^130807+1 = 1526465032849840942052993
2^130807+1 = 486552140243201573689
2^130817+1 = 675714563300731846571
2^130843+1 = 23415749153315254791213517097
2^130927+1 = 6720345000876501011
2^131009+1 = 337222115532246753452257
2^131041+1 = 94756828864670013737
2^131111+1 = 4134580064265494008220249
2^131149+1 = 2058573813879090154763
2^131203+1 = 11485335909484552667
2^131203+1 = 4608807453033761107579
2^131213+1 = 4480395049854197089283
2^131231+1 = 1449690052324264346120731
2^131293+1 = 4456614121954063177
2^131317+1 = 4158090709683842473
2^131357+1 = 27267528853728268801
2^131363+1 = 991871290979643956009
2^131381+1 = 16022567099737987644721
2^131413+1 = 104898861753259068899
2^131431+1 = 11586661541553362440055081
2^131431+1 = 1493018261087821241
2^131431+1 = 854287924841090737
2^131441+1 = 134061490732110029801659
2^131449+1 = 660979322776939057
2^131477+1 = 32442801060187363619
2^131477+1 = 9169191162895510177
2^131507+1 = 1878456481180320189131
2^131507+1 = 7369441625341798430805233
2^131543+1 = 751611778731653530282843
2^131561+1 = 377403700485346753
2^131581+1 = 652903415124239420633
2^131641+1 = 1046956550251161567859
2^131731+1 = 274458070639271081
2^131731+1 = 9216762775327900063486097
2^131777+1 = 60837541127866618150914731
2^131861+1 = 4073291166546743323073
2^131933+1 = 52198579281678351726251
2^131933+1 = 60106613239604555759459
2^131947+1 = 783129442513340497[/CODE]

 paulunderwood 2019-08-01 21:38

[QUOTE=GP2;520442]Congratulations on the PRP for 114743

There are smaller Wagstaff exponents with uncertified PRPs: 31601, 32369, 32377, 35677, 35851, 41269, 53759, 62581, 70921, 80819, 83423, 85517, 91159, 102299

There are also these uncertified Wagstaff prime exponents: 95369, 117239. Also the prime for 42737 has an old-fashioned certificate (that maybe can be verified with the Maple program, I'm not sure) rather than a Primo certificate.

A lot of work if anyone wanted to tackle it.

PS,
Also Mersenne PRPs with exponents 78737, 82939, 84211, 86137, 86371, 87691, 106391[/QUOTE]

[code]? ispseudoprime((2^41269+1)/3)
0
[/code]

 paulunderwood 2019-08-01 21:52

[QUOTE=GP2;520442]Congratulations on the PRP for 114743

There are smaller Wagstaff exponents with uncertified PRPs: 31601, 32369, 32377, 35677, 35851, 41269, 53759, 62581, 70921, 80819, 83423, 85517, 91159, 102299

There are also these uncertified Wagstaff prime exponents: 95369, 117239. Also the prime for 42737 has an old-fashioned certificate (that maybe can be verified with the Maple program, I'm not sure) rather than a Primo certificate.

A lot of work if anyone wanted to tackle it.

PS,
Also Mersenne PRPs with exponents 78737, 82939, 84211, 86137, 86371, 87691, 106391[/QUOTE]

[code]? ispseudoprime((2^41269+1)/3)
0
[/code]

Silly me. What is the cofactor? Answer on: [url]http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/WAGSTAFF_FF_with_factors.txt[/url]

 paulunderwood 2019-08-04 14:48

Done "W35851": [url]http://www.factordb.com/index.php?query=%282%5E35851%2B1%29%2F3%2F1184732147%2F1383891629171890065880777%2F54919454473787[/url]

 axn 2019-08-05 02:45

132k-133k

[CODE]2^132001+1 = 1233631356982642193
2^132019+1 = 11676365730006475259
2^132071+1 = 26871429497566200585283849
2^132071+1 = 6713891489149482227902993
2^132113+1 = 7826268976313187313
2^132157+1 = 34983030466439808324713
2^132199+1 = 84428471521478686316723
2^132247+1 = 8363359398567267547931
2^132257+1 = 1146021381367952923
2^132313+1 = 11836807971407883913
2^132329+1 = 13121494791879180529
2^132347+1 = 5131969476597623506291
2^132383+1 = 18296051320473285089
2^132383+1 = 3998892172972540849913
2^132403+1 = 2190196415278719721
2^132437+1 = 206260297243358898611
2^132439+1 = 224004281875426697
2^132439+1 = 238788002609980045594321
2^132439+1 = 368899493892384680527651
2^132469+1 = 293190053580584929
2^132541+1 = 46980021756603897461051
2^132607+1 = 433183846141292918899
2^132611+1 = 60210863712599153830681
2^132619+1 = 36147738048893812746971
2^132623+1 = 1718182949123519467
2^132679+1 = 24338378979651425021657
2^132689+1 = 98439752488856033
2^132701+1 = 3857600654202374092601476907
2^132721+1 = 625287293298930347945569
2^132751+1 = 1231762925124467369
2^132751+1 = 52685275118327026078939403
2^132763+1 = 1606088470184783131
2^132763+1 = 19316575800332994703369
2^132857+1 = 51484844551566998902812739
2^132859+1 = 1494857290283590903151627
2^132859+1 = 54321531026848772477579
2^132859+1 = 564243873913672889
2^132911+1 = 1794662420514931921
2^132929+1 = 17257581800468749603
2^132989+1 = 80638406019931908621710603[/CODE]

 axn 2019-08-16 07:40

133k-134k

[CODE]2^133087+1 = 453329102262294084723811
2^133109+1 = 3351248134854989099561
2^133109+1 = 36736921530912909763
2^133121+1 = 104201581276589219755481
2^133153+1 = 330553571607227777
2^133283+1 = 3549308659841553779607377
2^133283+1 = 7682849126487918604777
2^133319+1 = 250385176098144673
2^133319+1 = 4829643637184032939
2^133387+1 = 6342848219618436741377
2^133417+1 = 400313097624860129151977
2^133439+1 = 543243902132295186407161
2^133451+1 = 1612955449488790027
2^133481+1 = 99391448451815168641
2^133543+1 = 18663661033020198715202993
2^133543+1 = 36147461494085054457910529
2^133583+1 = 35456297117032534187
2^133649+1 = 49522392533768721059
2^133669+1 = 1114178544553122193
2^133709+1 = 719007773784874667
2^133831+1 = 151360784493193073
2^133843+1 = 1602938397236867909251339
2^133843+1 = 264072449460645848369
2^133853+1 = 41882464188467210441624291
2^133873+1 = 94516718399025953
2^133877+1 = 13538203739965294014649
2^133949+1 = 276349827110954772712561
2^133963+1 = 149899857045836076961
2^133993+1 = 54661018474564521924097
2^133999+1 = 136699326402532043
2^133999+1 = 83173639538609169883[/CODE]

 axn 2019-08-31 13:38

134k-135k

[CODE]2^134047+1 = 458551050120241153
2^134053+1 = 27938326875565281641
2^134089+1 = 66344718054731194051
2^134089+1 = 92566509206414883037797577
2^134161+1 = 7886156762440588666577
2^134171+1 = 266530723582396614123473
2^134257+1 = 197415670685852491
2^134257+1 = 3165550681360518348419
2^134263+1 = 53318470364671215113
2^134269+1 = 128604613958729177
2^134339+1 = 406367116822645339
2^134399+1 = 1463074782954436535969
2^134399+1 = 388878093712809981717990841
2^134437+1 = 167164161088501937267521
2^134591+1 = 271039207452607646489219
2^134591+1 = 405747390664898489
2^134593+1 = 41855356193894704121
2^134677+1 = 593955502467205138859
2^134681+1 = 63836537872015054200411956411
2^134731+1 = 20152946935171133641
2^134807+1 = 1415822143214064270259
2^134807+1 = 1738726745448518513
2^134837+1 = 3237446683991379428879923
2^134837+1 = 445780390413190969009
2^134873+1 = 1458440525691571848850219
2^134873+1 = 205758686362155200584964723
2^134909+1 = 413735673912308929[/CODE]

 axn 2019-09-14 11:33

135k-136k

[CODE]2^135043+1 = 123303916692400034900377
2^135043+1 = 46932312558114182811329
2^135049+1 = 951114340402710131
2^135089+1 = 198042930307632426296689
2^135101+1 = 88923883105222936307
2^135277+1 = 13844776221479612391359371
2^135277+1 = 679855536257354497
2^135329+1 = 88819179686681454611
2^135353+1 = 539390878052607511081
2^135367+1 = 1424221120037978369
2^135403+1 = 404374137201466757974720371218930399789339
2^135409+1 = 10075388732614430321
2^135467+1 = 3048199543152586499
2^135497+1 = 4087170515698284803
2^135497+1 = 59754231852741041281
2^135533+1 = 64503922863684527202961
2^135581+1 = 1637695521606285073
2^135593+1 = 2477273653317372437085403
2^135607+1 = 2317576572399241082939
2^135607+1 = 45893256909212164394587537
2^135617+1 = 226425059354163492883
2^135617+1 = 6828708088740832339
2^135623+1 = 5408603765659842193
2^135647+1 = 5025057265217846077583569228961
2^135649+1 = 11312844108831608873
2^135649+1 = 2021824423274156793806011
2^135661+1 = 714971474894103017
2^135719+1 = 960126630499930509804401
2^135727+1 = 468768835964743987
2^135757+1 = 6036810497331614963
2^135781+1 = 511534316793850921222153
2^135787+1 = 4158839988816074835153523
2^135829+1 = 276641211647482515499
2^135851+1 = 37648782586804124475299761843528048620693787079441528872193
2^135851+1 = 9912215698640939767969
2^135851+1 = 991795322102135777
2^135893+1 = 176202089257358120329
2^135913+1 = 1007816287916049673
2^135913+1 = 166555091819125207118299
2^135977+1 = 63277326542273164817[/CODE]

 axn 2019-09-29 02:05

136k-137k

[CODE]2^136027+1 = 3027599141758609819
2^136043+1 = 325842482373398219
2^136139+1 = 951503412092958217915913
2^136189+1 = 11563589698961263993
2^136189+1 = 959641937031951347
2^136193+1 = 37733407716702752009
2^136303+1 = 23265971948486843561
2^136303+1 = 3580357798007590183217
2^136319+1 = 82470779166238979216473
2^136397+1 = 144776139445280228105641
2^136453+1 = 156711957441178049
2^136453+1 = 474287986813848073609
2^136541+1 = 8476499283711862241
2^136603+1 = 15402453301791689027
2^136651+1 = 192707313094821563
2^136693+1 = 1044830121654814211
2^136727+1 = 109985911945908882195547
2^136753+1 = 17817248396750009861539618273
2^136753+1 = 29847412617949680673
2^136813+1 = 2413491717791990987
2^136841+1 = 303916128847568363717659
2^136849+1 = 1009138986256845482763787
2^136849+1 = 36274808869332645467
2^136861+1 = 230307114859192177
2^136889+1 = 13199868500333955928121
2^136889+1 = 149116525235882371
2^136889+1 = 947513007463808816916433
2^136897+1 = 278362767808056634481
2^136949+1 = 725457158703046706530409
2^136951+1 = 206772060714324753397681
2^136963+1 = 5027181616178147347
2^136979+1 = 983224043380450049
2^136991+1 = 13724303468553156379
2^136993+1 = 288960060670846541203
[/CODE]
Taking a temporary break.

 GP2 2019-09-30 04:05

[QUOTE=axn;526854]Taking a temporary break.[/QUOTE]

Thanks for all your efforts up to this point.

As always, Wagstaff-related data is available at [url]http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/[/url]

 GP2 2019-10-10 21:13

2^5743+1 is now fully factored. However, M5743 is not.

Exponents 7417 and 8849 are fully factored as both Mersenne numbers and Wagstaff numbers. Almost a year ago, I wondered if that wasn't a coincidence (click on the > icon below to read the reasoning in the original post).

[QUOTE=GP2;500262](Click on the > icon to read the original post)[/QUOTE]

I started doing deeper ECM on Wagstaff exponents under 10k, to try to create new cases where the same exponent was fully factored in both cases.

So far I've found 61 new Wagstaff factors for very small exponents, but only two of them resulted in new PRPs: exponents 5261 and just today, 5743. And of course various people including Ryan Propper have been finding new Mersenne factors for very small exponents with much deeper ECM.

But there are still no doubly fully-factored exponents other than 7417 and 8849 (and much smaller exponents where it's hardly unusual for them to be fully factored, the largest of which are 1193, 1279, 1459).

 axn 2019-10-11 16:13

[QUOTE=GP2;527692]2^5743+1 is now fully factored[/QUOTE]
... and certified.

Congratulations:bow:

 axn 2019-12-04 13:42

137k-138k

[CODE]2^137131+1 = 265192503004348610276393
2^137209+1 = 325448681397255884371
2^137219+1 = 2301308500567444738609
2^137239+1 = 9819212986550632433
2^137251+1 = 111839258802768975126521
2^137359+1 = 19692787436755739729
2^137387+1 = 191500409981045273
2^137437+1 = 12424045758414564820272889
2^137437+1 = 140380469176933313
2^137437+1 = 17273129105552341649
2^137437+1 = 3251904111129641131
2^137443+1 = 518201485359944387
2^137447+1 = 40910441205871188257
2^137453+1 = 38617754679653469401
2^137483+1 = 2645734560747394049
2^137491+1 = 11736790270878540543431051
2^137491+1 = 16122173996427013313
2^137507+1 = 536832885187840618448921
2^137567+1 = 5130855963228473
2^137587+1 = 31331429139299
2^137597+1 = 42510106685163097
2^137653+1 = 17966607213001
2^137707+1 = 13370301643695611
2^137707+1 = 592758373181385446377
2^137713+1 = 678116686045697
2^137723+1 = 7452253650510043
2^137771+1 = 721746915583691
2^137827+1 = 10001873225057422727353
2^137831+1 = 1045210024504627
2^137869+1 = 388943275849304602980612139
2^137873+1 = 1762495764078694161203
2^137983+1 = 5306718932989217
2^137993+1 = 15312867978376758099137[/CODE]
There will be some known factors as factordb was not available while preparing the worktodo.

 axn 2019-12-13 09:11

138k-139k

[CODE]2^138007+1 = 10582086549836801291
2^138053+1 = 380792657401641191687521
2^138373+1 = 2610131839658149123475611
2^138403+1 = 5736695208051537601
2^138461+1 = 3207292823618646813155881141259
2^138511+1 = 71883818725201402005731
2^138547+1 = 16766226123181039390883
2^138547+1 = 8635412590464642058939
2^138563+1 = 1552890640069632336467
2^138581+1 = 85040022771016627
2^138599+1 = 118700921877185607716041
2^138629+1 = 2094111627438975931
2^138629+1 = 321906673282915619
2^138647+1 = 28163071861713235384403
2^138661+1 = 52676191348661515790969243
2^138683+1 = 7098795005607261331
2^138793+1 = 30267921156976098993953
2^138797+1 = 814989689103951189023617
2^138799+1 = 144772705260460775784401
2^138841+1 = 1723171067798010113
2^138863+1 = 10906437909197106257[/CODE]

 axn 2019-12-28 06:06

139k-140k

[CODE]2^139109+1 = 232901527497762293385571
2^139121+1 = 2748135663696293579
2^139123+1 = 144834293192245512587
2^139133+1 = 135249101784022350964739
2^139169+1 = 6833785971336806122647841
2^139273+1 = 403707106206774067
2^139291+1 = 176731201325093882563
2^139303+1 = 21161845438388854327561
2^139333+1 = 3780919371435556323569
2^139393+1 = 41915218600911416707
2^139423+1 = 192692015044480459
2^139423+1 = 7914151425713333513
2^139429+1 = 164938712030987651
2^139457+1 = 1604057597011403803520833
2^139457+1 = 27559316522031652297
2^139483+1 = 16141276954868227553
2^139511+1 = 823522945729052939
2^139547+1 = 168286091283720731
2^139619+1 = 4814315853824769913
2^139661+1 = 22143916187498246166089
2^139663+1 = 3195615102067962988012121
2^139681+1 = 642638717263461947699059
2^139697+1 = 2473244696010346349209
2^139703+1 = 1732287483485125979
2^139709+1 = 80900761562355467
2^139721+1 = 14093748534448965379378753291
2^139729+1 = 425779850240099253523
2^139747+1 = 4435439168292693329
2^139801+1 = 172147453827121182961
2^139837+1 = 133923044162410483
2^139907+1 = 11590132907577462409
2^139907+1 = 2327308434820250857
2^139907+1 = 61337367506195041571
2^139921+1 = 75969755935623092048369
2^139991+1 = 2474496757849085982827[/CODE]

 axn 2020-01-11 11:56

Another t25 on 137k-139k

[CODE]2^137147+1 = 28894310756788960796853689
2^137153+1 = 925985372364737241928601
2^137413+1 = 1403935141664544940921627
2^137413+1 = 4443801572645338006979
2^137483+1 = 190159853041802194800331
2^137597+1 = 43987475667364577473063283
2^137633+1 = 2804620285384763160341723
2^137743+1 = 201474912510791815628126963
2^138163+1 = 18292524171995335882906688539169
2^138449+1 = 525002284628826303656299
2^138563+1 = 14262822575931023754694057
2^138577+1 = 248056677547191379189283
2^138599+1 = 14738540602990299961765057
[/CODE]

 axn 2020-01-26 01:53

140k-141k

[CODE]2^140111+1 = 77469284497815491
2^140143+1 = 592025513761215614723
2^140159+1 = 201467685247372834503139
2^140171+1 = 165010002321185686148141873
2^140171+1 = 24883847191150226127323
2^140171+1 = 457792593598348274364073
2^140177+1 = 12329558734993518821249
2^140177+1 = 77923023130078393
2^140197+1 = 4300595712823998811387
2^140263+1 = 468194399927393841259
2^140263+1 = 654194182725875075083
2^140281+1 = 3512267339194889129
2^140317+1 = 8536959327824068112372867
2^140321+1 = 1429044649560657282913
2^140363+1 = 2678995580320549649
2^140411+1 = 258106569339322024955985371
2^140449+1 = 76953187839293611
2^140527+1 = 3604491079802500927793817841
2^140663+1 = 302699407146778787
2^140681+1 = 10563113688128573939
2^140689+1 = 65386496610925103219
2^140759+1 = 186667618699742227258493683
2^140773+1 = 19686201193345030864633
2^140773+1 = 6209039824790834939
2^140779+1 = 2703965316548356213237067
2^140797+1 = 1230255056261689534481
2^140797+1 = 46819597570303119203
2^140813+1 = 13556734180966701449
2^140839+1 = 3347242760080362037787
2^140839+1 = 523412640906952766129777884481
2^140909+1 = 16905298575736721041
2^140939+1 = 240834994853876613643
2^140983+1 = 2803367701832174293409
2^140983+1 = 509192399149446479539[/CODE]

 axn 2020-02-13 11:27

[QUOTE=axn;500831]Thus (2^35677+1)/3 = 1174478776290172030409 · 4519369329719894060013787 · PRP10694[/QUOTE]
This is now proven in factordb.

 axn 2020-02-15 03:38

141k-142k

[CODE]2^141041+1 = 2620852506580681647899
2^141041+1 = 432627872365974073
2^141067+1 = 12473620268302403953
2^141073+1 = 171056631286303596947
2^141121+1 = 14255755386359273508072137
2^141179+1 = 32735785754552406108504947
2^141199+1 = 711341112359339107
2^141233+1 = 69203266391109231371
2^141277+1 = 18009270784229410416377
2^141311+1 = 103878038212101680617
2^141353+1 = 297786171068390743489
2^141403+1 = 261054426370674323341995577
2^141461+1 = 1477944056551198412358379
2^141461+1 = 28821514094580112130964001147
2^141481+1 = 2270226665662101491
2^141481+1 = 23066176834150407226201
2^141497+1 = 68473357403054309627
2^141587+1 = 134453385548685126074731
2^141587+1 = 36985977508639324154329
2^141613+1 = 1021698454552918829275283
2^141619+1 = 114758835028570153
2^141619+1 = 210199486771384867747
2^141629+1 = 7836876375402353057
2^141667+1 = 2039705280450899779
2^141677+1 = 6422151172151052701617
2^141697+1 = 3466971263618776729
2^141719+1 = 136364179740920922289
2^141803+1 = 4266032592489353376921523
2^141811+1 = 22355887789813221348641
2^141851+1 = 9077150562092404076297
2^141853+1 = 3214741943823258180337
2^141863+1 = 169272377032791424243
2^141917+1 = 1202909672415437531
2^141941+1 = 342848575198683977
2^141959+1 = 2026070008002487427
2^141959+1 = 2285089841203108649
2^141959+1 = 765001165326817169
2^141959+1 = 89604484448023684571[/CODE]

 axn 2020-03-02 13:04

144k-150k

[CODE]2^144031+1 = 1346818327032288891234137
2^144061+1 = 6449808395236452301243
2^144167+1 = 2670210131612236876339
2^144173+1 = 3432702862468608557539153
2^144247+1 = 50668228045748162723
2^144259+1 = 983517151724581844137
2^144271+1 = 162736418454954297629657
2^144271+1 = 180794576320180547
2^144289+1 = 28486628460254942953
2^144289+1 = 32022727944367664322529
2^144289+1 = 97738832337649942658641
2^144451+1 = 104874118912521482401734697
2^144461+1 = 3365354950275676615027
2^144497+1 = 23344859151749635762859
2^144511+1 = 614809523618094222057931
2^144541+1 = 162723742163087379433763
2^144563+1 = 839116504851462140113
2^144569+1 = 56647098852395497169
2^144611+1 = 124441732201421651
2^144659+1 = 150946918635583481697329
2^144709+1 = 12312748945061284691
2^144731+1 = 111661512435292292651699884311043
2^144791+1 = 315995836324863387571
2^144817+1 = 693576770423492206081
2^144889+1 = 1451856430100748382411
2^144889+1 = 2546673294246750985081
2^144899+1 = 142113108733327947152440091
2^145007+1 = 671781857498491451
2^145031+1 = 464524624624409801
2^145109+1 = 178056584626512041
2^145133+1 = 7838289620534443768274227723
2^145139+1 = 515184682469692483
2^145219+1 = 91405622692618997419
2^145283+1 = 17281371712980884478257
2^145349+1 = 1842604149003083197817
2^145349+1 = 418709816357290021393
2^145417+1 = 10477542805408802391041
2^145487+1 = 359395009899752570729
2^145513+1 = 822340904655645121
2^145517+1 = 67567031770599578801
2^145547+1 = 1801588059475152131
2^145549+1 = 8216446651614329839048581271969
2^145679+1 = 40411922853512158969
2^145687+1 = 4229913688171090411
2^145687+1 = 59028817370396567967563
2^145709+1 = 111171792256670461331
2^145721+1 = 15478797745527231073187
2^145723+1 = 3432327919360275227
2^145807+1 = 148863400485389617
2^145903+1 = 38699131857494203675513
2^145967+1 = 85901630970007739
2^145969+1 = 1000767256825990210100081
2^146011+1 = 315306243347356243
2^146023+1 = 693702086988973537
2^146099+1 = 147597815946211540361
2^146141+1 = 534806376439785743089
2^146141+1 = 7196243856562016699
2^146191+1 = 311743846654631474618617
2^146203+1 = 26595489414718899011
2^146213+1 = 21497221347283955089
2^146249+1 = 15525392057871050546729
2^146291+1 = 29548557204299871233
2^146297+1 = 11407949095166903129
2^146323+1 = 74250892540338544619
2^146323+1 = 767798206743472825187
2^146323+1 = 9533120305158570099381519643
2^146347+1 = 1423415471102092303767721
2^146347+1 = 1960740311239689109361963
2^146381+1 = 10347336557708524291
2^146389+1 = 3795473728857007099907
2^146477+1 = 13380512283834293617
2^146477+1 = 22054326897600051454459
2^146513+1 = 994000231268148109115491
2^146519+1 = 7215865629103975817
2^146539+1 = 201009905948905109350667
2^146563+1 = 1946620296044125009459
2^146581+1 = 122950691181679259
2^146617+1 = 120475736930324836075153
2^146617+1 = 1942521620528417874697
2^146639+1 = 1055711893514396734342963
2^146647+1 = 306975855940847659
2^146647+1 = 537544014907719017531
2^146681+1 = 38807300651071378681
2^146767+1 = 1437044755015476437442553
2^146767+1 = 147254093703049885003
2^146767+1 = 363416850727892249
2^146801+1 = 56116563625181250329
2^146857+1 = 128187746685653750890623281
2^146917+1 = 274344814322655833
2^146917+1 = 35864312446758681547
2^146941+1 = 777249228718977080569
2^146989+1 = 329708399953568099
2^146989+1 = 513965499576399529
2^147011+1 = 101483536460247679382737
2^147029+1 = 85634447279652737
2^147197+1 = 1000843886016268361
2^147209+1 = 1047874471486268953410937
2^147221+1 = 8319227414690030625859
2^147253+1 = 16601960181416168203523
2^147253+1 = 192533953473308809049617
2^147331+1 = 39163880601898009313859857
2^147391+1 = 245526105203705617
2^147397+1 = 26335007405828482512329
2^147419+1 = 27095654489267658551329
2^147449+1 = 4031265419679094699
2^147451+1 = 164233004230689203
2^147451+1 = 512231938179300169
2^147517+1 = 1984235048153977802751545489
2^147547+1 = 700704301809138899
2^147571+1 = 14102699130679947097893137
2^147583+1 = 170320054652875377242245307
2^147583+1 = 328980393023691309721
2^147617+1 = 18256349804900246209
2^147647+1 = 39589939676826790819
2^147671+1 = 521448787879714422667
2^147703+1 = 15884484143877620782588747
2^147769+1 = 7163471145564308800193171579
2^147773+1 = 115136381549891659
2^147793+1 = 12874191584598982050838819
2^147827+1 = 4334375451880851107
2^147881+1 = 1654001961728154732179
2^147881+1 = 244697715450606093833
2^147937+1 = 93496984108982690867
2^147949+1 = 49948969640756668561
2^147977+1 = 46076756235781786547
2^148013+1 = 276340662896092283
2^148021+1 = 2797328848643505899
2^148063+1 = 115043884877285079979
2^148091+1 = 1007142808750497827
2^148091+1 = 1206927564537489859
2^148091+1 = 6650273367598416043
2^148153+1 = 116032440677951012986385057
2^148193+1 = 34451852066961570763337
2^148229+1 = 203744832124136089
2^148279+1 = 95265398410422919859
2^148301+1 = 124645536800926978411228457
2^148339+1 = 1454425434321115746264726451
2^148361+1 = 1958819230849979234657923
2^148403+1 = 13488914142914534840393
2^148403+1 = 153630076047278177689
2^148439+1 = 90869410250353366767307
2^148469+1 = 477554084369983163
2^148483+1 = 312467697553493219203
2^148501+1 = 4671286725547935072499
2^148513+1 = 11604082822374274849
2^148549+1 = 10075832407785156081257
2^148579+1 = 194710496835357827
2^148633+1 = 133226577808194397565371
2^148639+1 = 462206146038559525483
2^148639+1 = 953021486532981215183257
2^148667+1 = 159209812876967561
2^148667+1 = 94176887419512981019
2^148667+1 = 94936246181909261239428161
2^148669+1 = 150876984539991313
2^148747+1 = 106893758805118771
2^148781+1 = 5117735018123876260547
2^148783+1 = 95752828664341218762059
2^148817+1 = 46419498076934320083601
2^148859+1 = 827693016345463987
2^148867+1 = 86546956508572950496289291
2^148913+1 = 427098515294536721
2^148927+1 = 216787490679898937865251
2^148961+1 = 246451389577244651
2^149033+1 = 116484115313868443
2^149113+1 = 388603143597861347
2^149113+1 = 6177520262290818086358227
2^149119+1 = 1147834783719148352069989193
2^149161+1 = 25303915279767602822153
2^149161+1 = 72478162225838051
2^149183+1 = 204429269406361092420923
2^149213+1 = 21899468880913136977
2^149213+1 = 71333837283244225040700689
2^149249+1 = 259135329751131417375593
2^149251+1 = 14512002953086386703855507
2^149257+1 = 63007467460345343799813217
2^149287+1 = 148566558962016659
2^149333+1 = 2413495241628576811969
2^149371+1 = 4738802253508264121
2^149411+1 = 13347870082065921881
2^149423+1 = 13330197310612573571
2^149459+1 = 5056277604492093209
2^149491+1 = 531494357720617053467
2^149551+1 = 1315004599065306608116499
2^149551+1 = 64920473149258822219
2^149579+1 = 18935739778676988187
2^149579+1 = 7302727215996817651
2^149713+1 = 893426408629704429714497
2^149767+1 = 6938399419063980993790409
2^149837+1 = 16554086541087228803833
2^149839+1 = 2124520846971393587
2^149867+1 = 16952422517979753137
2^149893+1 = 87870325308152461241273
2^149909+1 = 174255585857348131
2^149921+1 = 94722291236911721
2^149953+1 = 9029225117846772256177129
2^149969+1 = 184920473301953957353[/CODE]

 axn 2020-03-04 13:42

143k-144k

[CODE]2^143063+1 = 1062888329107817951153
2^143107+1 = 1581256646010490603907
2^143107+1 = 70057812048758090192737
2^143111+1 = 3099441880300832911176817
2^143141+1 = 1065792576054392089563460457
2^143141+1 = 8487806048895613801
2^143159+1 = 9621142696660504468577
2^143177+1 = 5722087166602655758378753
2^143239+1 = 117738298384130569
2^143263+1 = 88131704054937091
2^143281+1 = 929951706593956010539249
2^143287+1 = 96414089460152371
2^143291+1 = 1284366247573405889
2^143333+1 = 69698705203500884443
2^143387+1 = 81690385040278236193
2^143483+1 = 254714745462109608775249259
2^143489+1 = 10987488955121054860067
2^143489+1 = 98083217685173834001289
2^143501+1 = 624867179861689591483
2^143503+1 = 90589679727209274307
2^143519+1 = 1083463197116191033
2^143527+1 = 14274462381948746113
2^143569+1 = 15784815076066430929
2^143569+1 = 399822176322290199656107
2^143651+1 = 630122784863893422672689
2^143677+1 = 63176430206314740257
2^143677+1 = 89979050769494464651
2^143699+1 = 15366080406967957873
2^143729+1 = 113115592201702417
2^143729+1 = 9252867537045217296502619459
2^143743+1 = 6650197335292149266576393
2^143813+1 = 6551475246618385020667
2^143881+1 = 1693328605284339043
2^143971+1 = 178654089393032997404371
2^143977+1 = 138916388729072827
2^143981+1 = 38248796666238972193[/CODE]

 axn 2020-03-06 14:41

142k-143k

[CODE]2^142007+1 = 3269135105018339827
2^142031+1 = 2847496435422490729
2^142049+1 = 1099798333058790947
2^142061+1 = 23140548243032446139
2^142097+1 = 13109421298713023747
2^142123+1 = 135544878152711113
2^142123+1 = 14820126050013533129
2^142123+1 = 30088654985996130049
2^142151+1 = 83951997166317009361
2^142159+1 = 9063145980920869783531708481
2^142211+1 = 3071975256834034078387
2^142271+1 = 13828795217212025659003
2^142319+1 = 193336035201601057921
2^142369+1 = 1034226658047421801
2^142403+1 = 1832652477312818363
2^142403+1 = 208754581810125500400203
2^142403+1 = 2612923110894442431290521
2^142403+1 = 639885136942730912897
2^142421+1 = 293624544479899384117819
2^142433+1 = 18386164000121749730323
2^142453+1 = 235161714000636883
2^142537+1 = 6387864155566300003
2^142543+1 = 720574531636680916297
2^142591+1 = 83462838588173580138244729
2^142619+1 = 134452229102958737
2^142619+1 = 4659246248989501361
2^142619+1 = 98772191261608283
2^142657+1 = 451494702127052873
2^142657+1 = 73200231605791923067
2^142697+1 = 1342684155218742532147379
2^142771+1 = 655625909373202558021049579
2^142787+1 = 337270804971772452139
2^142787+1 = 4556958736414575611
2^142789+1 = 34737903436870620297659
2^142789+1 = 454336902948567593
2^142789+1 = 5965670430754477368803569
2^142811+1 = 7120969024154927078787953
2^142867+1 = 1305153419208130942963
2^142873+1 = 349148565202212571
2^142903+1 = 986780570430220600402579
2^142963+1 = 7704014438684018414257
2^142973+1 = 1148767019165329723811
2^142993+1 = 203113846544490458407811
2^142993+1 = 36396663015360095518544083[/CODE]

 axn 2020-03-07 03:28

150k-156k

[CODE]2^150011+1 = 573047777894714651
2^150067+1 = 331111702885501879489
2^150077+1 = 32602793126938503843043
2^150083+1 = 2348866219815346027
2^150083+1 = 2841977535974826774419
2^150083+1 = 613778120564961357667
2^150091+1 = 344224283042887035353
2^150091+1 = 9527802743759957268019
2^150217+1 = 75463279615078396537
2^150299+1 = 40833982151482698423457631270095793
2^150323+1 = 17972980845421743593
2^150377+1 = 438749417770425636362017
2^150379+1 = 38245846352511371009
2^150379+1 = 699654307053275099667721
2^150427+1 = 5312939239867454851
2^150439+1 = 25143347636431409730041
2^150497+1 = 19910835595589425867
2^150533+1 = 3055318528255668746299
2^150551+1 = 175424212578061651
2^150589+1 = 41933579731667131688083
2^150617+1 = 24322085969454234304307
2^150617+1 = 31010169371328702869597611
2^150697+1 = 15942730455035457509980884299
2^150707+1 = 66049821126388336673
2^150743+1 = 146054688446310157201
2^150767+1 = 184591395476228483
2^150827+1 = 2077587793487742296659
2^150901+1 = 3569019055046784467
2^150919+1 = 207686567782487950577
2^150919+1 = 8057134874646372313723
2^150991+1 = 3107129524339068427
2^151027+1 = 972380854032508232236001401
2^151051+1 = 35235242015216648583331
2^151121+1 = 279209210308355521
2^151153+1 = 528689688016845539
2^151153+1 = 682186836630383541889
2^151171+1 = 5386533501595226422171
2^151189+1 = 21061673621132368481203
2^151253+1 = 264757418907443633
2^151279+1 = 1162800751126911316270027
2^151391+1 = 225449288253508142441857
2^151423+1 = 369960182170461537121
2^151429+1 = 20872142069322914339
2^151451+1 = 112156282198491570569
2^151451+1 = 809679338453134913
2^151477+1 = 145174515696155369
2^151483+1 = 533507098206365131
2^151517+1 = 4742431465274888132441
2^151597+1 = 3905360021812391473
2^151603+1 = 6668887153195460020287403
2^151637+1 = 811317669075974209
2^151681+1 = 18767064217520494097
2^151703+1 = 307751360159301762855377
2^151769+1 = 1075008490621664887129
2^151769+1 = 2674618970196927857
2^151909+1 = 5832855110821994550158401
2^152077+1 = 6411579011794380491
2^152093+1 = 9142087646558317775251
2^152189+1 = 477047745241438529
2^152219+1 = 713129228321479845683
2^152239+1 = 51062678463487157704537
2^152267+1 = 69656738939086938491
2^152363+1 = 1202905792653771372623970977
2^152377+1 = 45325164719530957483
2^152389+1 = 267094448166384907459
2^152389+1 = 459156942516098681
2^152389+1 = 6318407388895077979
2^152417+1 = 19655386695652270427
2^152417+1 = 4316414076745692011
2^152423+1 = 381597814031583641
2^152461+1 = 40547016968766301918451
2^152533+1 = 763656399085307753
2^152597+1 = 58592204616151230737
2^152657+1 = 227627430141421747938184513
2^152657+1 = 3403222734478081379
2^152681+1 = 1478559337477992663601
2^152767+1 = 2566365337545287524601
2^152783+1 = 276789466376381033
2^152819+1 = 125472965581704116137
2^152857+1 = 2141578029214632383882959481
2^152897+1 = 31709573922618926609203
2^152939+1 = 145325941401654185251
2^152939+1 = 46739323182525942193
2^152989+1 = 772288630539440921
2^152993+1 = 104385077854846193
2^153001+1 = 57965124199948647203
2^153059+1 = 3897282942406049455891
2^153067+1 = 96743775449938979
2^153107+1 = 440641263567082366961
2^153113+1 = 495912062827374131
2^153133+1 = 22328586328807555296043
2^153137+1 = 178198916865435971
2^153247+1 = 6099242312215824857
2^153259+1 = 7962247774799420760083
2^153259+1 = 826517322538227427
2^153277+1 = 105311936068197361
2^153277+1 = 9669588057949993697
2^153281+1 = 214605362480855077603
2^153281+1 = 486263254108398083
2^153287+1 = 53731263773344880915747
2^153313+1 = 461323983201481140067
2^153319+1 = 835531789854882347
2^153409+1 = 26350668529451751893033
2^153427+1 = 49024025154220391965633
2^153437+1 = 847618079579626123
2^153457+1 = 177897800533497593
2^153469+1 = 293995100741909467
2^153523+1 = 1054395758704784750843
2^153523+1 = 1675602064531792547
2^153529+1 = 11948858928152015753899
2^153607+1 = 4943327887437008494571
2^153623+1 = 30802067382552576718918889
2^153749+1 = 1217006262707303167427
2^153757+1 = 11453921637044343659
2^153763+1 = 46631000085232346723
2^153763+1 = 601050904710345821191961491
2^153911+1 = 1781109496515190481822801
2^153913+1 = 31559576275527186758153
2^153929+1 = 120795401782112745643
2^153929+1 = 304583821163947219
2^153929+1 = 57279587117301897841
2^153947+1 = 2001787304486091550050735577
2^154057+1 = 9812455476975422321
2^154067+1 = 4550398642432900561
2^154073+1 = 48174489914123911245553
2^154087+1 = 10965835118615083153
2^154087+1 = 4124840913728561561
2^154181+1 = 359971669852745381867
2^154183+1 = 87558227230012274831993
2^154183+1 = 986643674702346928051
2^154213+1 = 5535745862630198843
2^154267+1 = 6873471550380087803
2^154277+1 = 549916322750720662393
2^154303+1 = 68260914175386419699533530427
2^154313+1 = 11252462872481437462755166499
2^154313+1 = 61628756858489096098681
2^154333+1 = 4038819409302697531
2^154417+1 = 2315377241877736317587
2^154573+1 = 127280495016888737
2^154573+1 = 4211029210362176953
2^154573+1 = 47470102709094021731
2^154621+1 = 39102658022316396197536500299
2^154667+1 = 23085706736767653680699
2^154691+1 = 2202008104224530536056481
2^154747+1 = 93735414762997067
2^154787+1 = 55480765254364118323
2^154787+1 = 84037770692491459
2^154789+1 = 10141758081771256842360113
2^154849+1 = 351388654997372536667
2^154873+1 = 9998141789792430683483
2^154883+1 = 1711171809624897749243201
2^154933+1 = 122849650656621662863403
2^154943+1 = 116357234525357214997809889
2^154943+1 = 59814621454506133697
2^154981+1 = 269420521241384916673
2^154991+1 = 1238947803791013499
2^155009+1 = 3170274457239702437843
2^155083+1 = 191573830621159795841083
2^155083+1 = 276892483752337107539
2^155119+1 = 401169710462407787
2^155201+1 = 4677677407762343009
2^155203+1 = 227892353649256811
2^155251+1 = 623087994070179652657
2^155303+1 = 2155964169772441656694379
2^155381+1 = 67840595582781742606441
2^155399+1 = 275364707708394368769217
2^155423+1 = 1632465870340194054955873
2^155443+1 = 47808266055986820620603
2^155453+1 = 322656768524717329699369
2^155473+1 = 8996313639908536478179
2^155537+1 = 27025063674284332891841
2^155539+1 = 2137384962709192167889
2^155569+1 = 191339523767590880723
2^155569+1 = 282868722516754147045931
2^155581+1 = 22005026945924866759340220569
2^155581+1 = 264269978973861386689
2^155621+1 = 47412381351568916651
2^155653+1 = 11415770261858817691
2^155689+1 = 4611846059187280129
2^155717+1 = 132449328144296626241
2^155723+1 = 2114804785506275587931
2^155777+1 = 251652458091299266867
2^155777+1 = 267276860202858395598649321
2^155797+1 = 63900339911538133387
2^155851+1 = 88345590888087711516980123[/CODE]

 axn 2020-03-12 02:35

156k-157k

[CODE]2^156041+1 = 432612818295529969
2^156061+1 = 17325703762025411966908403
2^156061+1 = 2128608501291999313
2^156139+1 = 439759561973002361
2^156139+1 = 79059396532266571
2^156151+1 = 12650348911211512520603
2^156151+1 = 821302031930413524763
2^156257+1 = 16472459043143141238539
2^156269+1 = 134769379663657936787
2^156361+1 = 1047468997559695331
2^156361+1 = 4255024606852832190152171
2^156487+1 = 3083446104681151565134091
2^156491+1 = 11602590581074772483
2^156491+1 = 248725255412607489023017
2^156491+1 = 262561119150494252642296891
2^156493+1 = 211677004038766771
2^156521+1 = 137669769196817041
2^156521+1 = 5621729414063489710057
2^156521+1 = 79409138321831587
2^156593+1 = 1351131451473643529
2^156677+1 = 237467386363791809
2^156677+1 = 314793629835765309862513
2^156707+1 = 19136895781189840963
2^156707+1 = 2175601173831997817
2^156727+1 = 812715106204702873
2^156797+1 = 26584817489761133329
2^156841+1 = 314197565912393899
2^156887+1 = 6400188591676961801[/CODE]

 axn 2020-03-19 08:25

158k-159k

[CODE]2^158003+1=249786227179833520009
2^158003+1=665474340946481357537
2^158017+1=1769167683295943851
2^158077+1=1273613519957753081
2^158143+1=3915471922845463912483
2^158189+1=7088305570665088183966313
2^158209+1=4996790390062580107
2^158261+1=89913449024403385187
2^158269+1=2530978978619978197609
2^158293+1=18838498433433432354763
2^158371+1=11221946466370224803
2^158393+1=507408166963401413323
2^158407+1=2094791337285582475387
2^158419+1=2172932981241125923
2^158419+1=32099092482333779537
2^158449+1=336045309590340967417
2^158449+1=4354087343679254081
2^158567+1=4450441707374087651
2^158597+1=51614090146851350579
2^158647+1=710745111980243704722931
2^158657+1=95794102821883512499
2^158731+1=27188116256616894377
2^158747+1=9807296910519689209
2^158749+1=1718432161829816555987
2^158759+1=398276383450668853457203
2^158771+1=61388063642538708443
2^158791+1=1036632222546408733369
2^158791+1=709605570864439399361
2^158843+1=7322447500424285059
2^158909+1=16518214430293737115769
2^158923+1=932313682475814259
2^158959+1=1764977683106334882265563451[/CODE]

 axn 2020-03-27 10:28

159k-160k

[CODE]2^159017+1 = 2454134699283995081
2^159113+1 = 12870018826728951643603
2^159119+1 = 35299824268765877027
2^159157+1 = 19609253160866547121
2^159167+1 = 22526795678999214189611
2^159167+1 = 276481010365935895657
2^159191+1 = 187565647792815947
2^159191+1 = 2110498555472612177
2^159199+1 = 85268160637795228077691007291
2^159209+1 = 13382602093087440089
2^159223+1 = 1647715335225299729
2^159233+1 = 3519603692670355508478914009
2^159293+1 = 2101187844598959241
2^159319+1 = 16382043682710146751883
2^159361+1 = 11926277506372489429097
2^159361+1 = 443816980955328082673
2^159437+1 = 168488186106973651
2^159437+1 = 81612915939631083283609
2^159457+1 = 8629998803984459916307
2^159463+1 = 6435575318566261033
2^159469+1 = 264518970670446430421801
2^159469+1 = 344117051968727369
2^159473+1 = 159411074570837050217
2^159539+1 = 47572485809966527047571
2^159541+1 = 9758798264498832001
2^159569+1 = 18692679885800959986703326313
2^159571+1 = 44882404041663960329
2^159571+1 = 458197581889674192659
2^159571+1 = 844052637256869347
2^159589+1 = 77503064585266568436659
2^159617+1 = 3352354109004868675635331
2^159629+1 = 86708447613872498707
2^159673+1 = 1811931601037879833
2^159683+1 = 2091739452881597432993
2^159769+1 = 7130325067456867513
2^159779+1 = 2134254635405588728033
2^159791+1 = 1063570797474230579
2^159793+1 = 6002580082818354444611
2^159839+1 = 729113467236828139
2^159857+1 = 487664637169847243
2^159911+1 = 161652206434630534806971
2^159977+1 = 3220910966526862644793[/CODE]

 axn 2020-04-04 17:22

160k-161k

[CODE]2^160019+1 = 603140704182085163
2^160031+1 = 13081850164863059659
2^160091+1 = 42715387629804216507136699
2^160159+1 = 276865038732591220321001
2^160201+1 = 937972441809268504097
2^160217+1 = 1070441849002593807097
2^160253+1 = 121262271287521889299
2^160313+1 = 3423865867721420679220889
2^160367+1 = 120992713450704921307
2^160397+1 = 265076116108842617
2^160397+1 = 623964577544953387
2^160423+1 = 45387904567759499403997777
2^160453+1 = 5758007655845406855577
2^160483+1 = 113697618028904409044788403
2^160499+1 = 18034253364068346121
2^160583+1 = 5338182580039406203
2^160583+1 = 6322400053512929153
2^160637+1 = 18912725972664600121
2^160639+1 = 9667610200135609333907
2^160649+1 = 131615075755944606290779
2^160651+1 = 8952775814175372827
2^160687+1 = 245390015360059249
2^160697+1 = 141204548063299697
2^160709+1 = 15927278437130159387
2^160723+1 = 954138511065753404761333219
2^160757+1 = 5174179758718679404320827
2^160817+1 = 1005377664568849129211
2^160841+1 = 65430834387439767693520474409
2^160861+1 = 12094024187725689817
2^160933+1 = 2306859548319248201
2^160997+1 = 1836540618843376410299[/CODE]

 axn 2020-04-08 03:32

157k-158k

[CODE]2^157007+1 = 106284597660570529
2^157007+1 = 6221085133129795236601
2^157013+1 = 1336540242981100512861113
2^157019+1 = 142037433608417483735941403
2^157057+1 = 88210690743089387358113
2^157103+1 = 946892444485493808937
2^157163+1 = 468860040826087903448069833337
2^157189+1 = 7836646095660278194211
2^157207+1 = 80966306147997331
2^157211+1 = 2945350618002497321
2^157259+1 = 73727196176189814977371
2^157273+1 = 1576820432345652073
2^157279+1 = 2666524628454379534417
2^157363+1 = 5206103025496466227
2^157429+1 = 74969817964264393
2^157457+1 = 32378173696506995444489
2^157457+1 = 806021139618905733979
2^157477+1 = 3307793277021977889363131
2^157489+1 = 8923505899632281002373921
2^157523+1 = 578652430893330809
2^157543+1 = 1045813335484547453641
2^157543+1 = 269351625546559891
2^157571+1 = 170096616918127570249
2^157667+1 = 180443029438179643
2^157747+1 = 2915433184354534963129
2^157799+1 = 205515960105416128969
2^157831+1 = 1162606773539340473
2^157831+1 = 207748854609356937550547
2^157889+1 = 5704209146883199763
2^157931+1 = 181122459112536707
2^157931+1 = 990745345894520559073
2^157991+1 = 11251691611215984857
2^157991+1 = 3049264243829275561897
2^157999+1 = 669404333236985825627[/CODE]

 axn 2020-04-13 02:06

161k-162k

[CODE]2^161009+1 = 1285244140794421521019
2^161047+1 = 9636749650652145289
2^161059+1 = 40753765071655752329
2^161149+1 = 19555378403906250974521
2^161159+1 = 56785808187910375451
2^161167+1 = 366578454328086683
2^161233+1 = 96980073766755663083
2^161263+1 = 4616241924230444699
2^161281+1 = 186575914585554841
2^161333+1 = 423157945496493787
2^161339+1 = 13839694158944805199921
2^161363+1 = 17261428285657737674337353
2^161407+1 = 5003374317356637779057
2^161461+1 = 1251138697451078756707
2^161471+1 = 458452682602253363
2^161611+1 = 638727126554729273
2^161753+1 = 1309581246191857697
2^161771+1 = 48062896860683354513
2^161773+1 = 27763208247383581457
2^161783+1 = 30192460372605417899
2^161923+1 = 121091025711933290339
2^161969+1 = 116811974056477242451
2^161969+1 = 253488221788777270033379[/CODE]

 axn 2020-04-21 01:56

163k-164k

[CODE]2^163061+1 = 1456687377116065873
2^163151+1 = 46747116014899694161
2^163169+1 = 3584147938640756089
2^163181+1 = 830547447929138303009
2^163243+1 = 583686946676577921005891
2^163309+1 = 1719515193630333934634473
2^163351+1 = 138293482267111723
2^163351+1 = 779119426330739221297
2^163351+1 = 7992651520874930543587
2^163393+1 = 447392537194161760610531
2^163403+1 = 2063139648388734810481
2^163411+1 = 148711466948184644267
2^163417+1 = 4261875354849043969
2^163433+1 = 351367123456084963
2^163543+1 = 288783153584346883588553809
2^163621+1 = 807244637453088254021561
2^163643+1 = 16147796443694365633
2^163643+1 = 41573660574033060841
2^163697+1 = 1598199089022642049
2^163729+1 = 433431639623221888457
2^163771+1 = 12800370171446097774075889
2^163771+1 = 276440924456028553667
2^163811+1 = 292566849028790009
2^163841+1 = 137455313581868329
2^163841+1 = 4817780879509711464568339678859
2^163841+1 = 89966751121382060556979
2^163847+1 = 14478779855233896708721139
2^163901+1 = 101449674092145187
2^163909+1 = 176590425775359921763
2^163909+1 = 197194181387434271329
2^163927+1 = 456732212761660553
2^163991+1 = 2412407614015217587[/CODE]

 axn 2020-05-01 02:06

164k-165k

[CODE]2^164011+1 = 52304995292395941961
2^164071+1 = 34890944635611605297
2^164093+1 = 29703080004460764059
2^164117+1 = 648102045926649848899
2^164173+1 = 1708259499807228417856895833
2^164183+1 = 31705482582070487699
2^164183+1 = 437862518023744361
2^164183+1 = 7277037414615882313
2^164201+1 = 23227790610002565089
2^164201+1 = 458611738552698264526939
2^164209+1 = 1404412007010359177
2^164231+1 = 22266352817206998234457
2^164239+1 = 76779372226258171
2^164363+1 = 10224214364265619871813449
2^164363+1 = 320176300334660232403
2^164387+1 = 869345497259258232827
2^164413+1 = 77610551508163474488643
2^164431+1 = 23878507231626940481
2^164443+1 = 27572082935187041057
2^164503+1 = 1444920674389698286513
2^164531+1 = 75784782268694561137
2^164771+1 = 478440055937235626335433
2^164821+1 = 1834182958798727099443
2^164881+1 = 1232828794120019169737
2^164893+1 = 256403822370774203[/CODE]

 axn 2020-05-05 08:01

162k-163k

[CODE]2^162011+1 = 213509379861249167251
2^162059+1 = 13063097921781206939
2^162091+1 = 3397193220801518339
2^162109+1 = 3389966042900575297
2^162109+1 = 6153906272939644649
2^162143+1 = 570035892814661379284730179
2^162229+1 = 370833980478767177
2^162257+1 = 5126506483948850027
2^162359+1 = 35697350918260823611141691
2^162389+1 = 1164295382519382361
2^162413+1 = 343198668186332747
2^162413+1 = 7431827440004556451
2^162457+1 = 19179616101580750129
2^162499+1 = 242394335618845072075423697
2^162529+1 = 158692623854315033800101667
2^162649+1 = 1287832734692534249
2^162839+1 = 12254008819256443601
2^162839+1 = 16695965646838784809
2^162853+1 = 324122576971827041
2^162853+1 = 707356268132186867009
2^162881+1 = 1749287597871566579
2^162881+1 = 32608179381856720466819
2^162917+1 = 23808938703563707671097027
2^162917+1 = 25127411766198422528233
2^162947+1 = 702078678693160675097
2^162997+1 = 13513310116726405011251[/CODE]

 axn 2020-05-08 01:22

165k-166k

[CODE]2^165001+1 = 1604899594900215963659
2^165037+1 = 20249321029647611765051
2^165041+1 = 20798674024736073348409
2^165049+1 = 126567303562937713033
2^165079+1 = 172226206530896984211667
2^165103+1 = 5148905940827470292581171
2^165181+1 = 514787607054597306299
2^165211+1 = 6028324863478297400593
2^165247+1 = 711683038970704423818162001
2^165317+1 = 1810861012100539450283
2^165349+1 = 212848341882613688347
2^165437+1 = 10379239997556513049
2^165551+1 = 123637704917342850548929
2^165553+1 = 1815949954043196949493609
2^165589+1 = 925693565832824851
2^165611+1 = 424279030326550189749923
2^165667+1 = 1440275665389499520464409
2^165667+1 = 893605833129070253987
2^165701+1 = 7806912367183165441
2^165713+1 = 396862773825200777283107
2^165811+1 = 257172826640396883471111889
2^165811+1 = 39049184287828221747458873
2^165811+1 = 550782892876538474833
2^165817+1 = 1152407426138278561
2^165833+1 = 182133801378763179313
2^165883+1 = 25116361128278687510923
2^165901+1 = 37723750186698104902412947
2^165983+1 = 167758861257165706348243[/CODE]

 axn 2020-05-15 03:09

166k-167k

[CODE]2^166013+1 = 7825877047619303776897
2^166063+1 = 9089494195729805385761
2^166081+1 = 90885541098089118900697
2^166151+1 = 208995844710528179
2^166157+1 = 1421598601182202657
2^166183+1 = 547431097481234840788427
2^166189+1 = 71717471582894268473
2^166219+1 = 2891253674029415577497
2^166259+1 = 6795711321561088074851
2^166349+1 = 53729447665322130027427
2^166351+1 = 5587171207062266777
2^166417+1 = 324796066466509697057
2^166429+1 = 138522624958505773305451
2^166487+1 = 840999073356435071150549651
2^166601+1 = 41685695009467965373495313
2^166603+1 = 699629707919711831707
2^166631+1 = 149309249479714691
2^166657+1 = 1457988889909763787083
2^166657+1 = 220010060632326553
2^166657+1 = 41838589285783246531
2^166723+1 = 3056374665901254377
2^166739+1 = 13942330898975485263923
2^166783+1 = 198162352309679209369
2^166783+1 = 2290343007777739757123
2^166799+1 = 32406281802144344641675963
2^166849+1 = 3476970330724075445483
2^166849+1 = 39179631260007325677539
2^166853+1 = 256232054911458667
2^166853+1 = 5374355748022002511751444137
2^166909+1 = 165424187880449903210777
2^166931+1 = 545660868539092529
2^166967+1 = 4506921792269233749064139
2^166967+1 = 859067575169548099
2^166979+1 = 152299560439540081
2^166979+1 = 483085647486554702683
2^166979+1 = 51974335377728844208939
2^166987+1 = 16433209224330346489
2^166987+1 = 18202300168551240644017361
2^166987+1 = 389467374205159659803[/CODE]

 axn 2020-05-23 01:51

167k-168k

[CODE]2^167039+1 = 6510982994815432705297003
2^167051+1 = 5155445184151785091
2^167077+1 = 6334613439856296972457
2^167087+1 = 273951768297163554761
2^167113+1 = 4840744563119184984427
2^167177+1 = 93930179001792361
2^167329+1 = 17294833599317161633
2^167329+1 = 703291982012308464122785441
2^167429+1 = 227833642105485536587
2^167443+1 = 135613346880676001
2^167443+1 = 70011950720246543017
2^167483+1 = 99939840195326563
2^167521+1 = 87613085801487859823711257
2^167521+1 = 94039053459743273513
2^167623+1 = 2794445439465183923
2^167633+1 = 8280701536593076771
2^167641+1 = 2534607273404184965377
2^167663+1 = 33700558947770094286603
2^167663+1 = 934369237663928278649
2^167683+1 = 538914080679215682281
2^167711+1 = 312079280027813833
2^167747+1 = 1443502969244044561
2^167747+1 = 4884332356104345167558729
2^167801+1 = 119972049727136947
2^167861+1 = 2087222500539363809
2^167873+1 = 7331198911639528361
2^167891+1 = 38902532197087303411
2^167953+1 = 81262728927839701142947
2^167971+1 = 2568632610402734857[/CODE]

 kruoli 2020-05-26 22:38

Hey, I'm proposing to change the "factor found" lines slightly:
i. e.
[QUOTE]2^167747+1 % 1443502969244044561 == 0[/QUOTE]
because
[CODE]2^167747+1 = 1443502969244044561[/CODE]

is not true; yes, it is a shorthand.

Any suggestions are welcome.

 paulunderwood 2020-05-26 22:46

[QUOTE=kruoli;546543]Hey, I'm proposing to change the "factor found" lines slightly:
i. e.

because
[CODE]2^167747+1 = 1443502969244044561[/CODE]

is not true; yes, it is a shorthand.

Any suggestions are welcome.[/QUOTE]

If anything A | B is preferable and shorter.

 kar_bon 2020-05-27 00:52

Or like this:
[C]
p k
167747 4302619329240
[/C]
with factor = 2kp+1 of exponent p.

 axn 2020-05-27 01:50

I use the N = f notation because factordb supports it. Are any of the other notations supported by factordb (for bulk submitting results)?

 paulunderwood 2020-05-27 05:24

[QUOTE=axn;546558]I use the N = f notation because factordb supports it. Are any of the other notations supported by factordb (for bulk submitting results)?[/QUOTE]

Fair enough. It is just a polymorphed symbol.

 axn 2020-05-27 07:52

[QUOTE=paulunderwood;546567]Fair enough. It is just a polymorphed symbol.[/QUOTE]
[C]grep has results.txt | cut -d' ' -f3,7 | sort | uniq | sed -e's/ / = /'[/C]

This is my secret sauce. If you can give me one for the [C]f | N[/C], I can run both, use one for factordb and post the other here.

 paulunderwood 2020-05-27 08:14

[QUOTE=axn;546568][C]grep has results.txt | cut -d' ' -f3,7 | sort | uniq | sed -e's/ / = /'[/C]

This is my secret sauce. If you can give me one for the [C]f | N[/C], I can run both, use one for factordb and post the other here.[/QUOTE]

[c]grep has results.txt | cut -d' ' -f7,3 | sort | uniq | sed -e's/ / \| /'[/C]

Should do it

 kruoli 2020-05-27 08:39

[QUOTE=paulunderwood;546569][c]-f7,3[/c][/QUOTE]

Unfortunately, that does not invert the order in a line. I'd propose:
[code]grep has results.txt | cut -d' ' -f3,7 | sort | uniq | sed 's/^\([^ ][^ ]*\) \([^ ][^ ]*\)/\2 | \1/'[/code]
(I'd be using the "c" tag but that gave weird formatting, how can I escape square brackets?)

The result seems a bit chaotic, because the first column has no constant size. One could solve that using e.g. [c]xargs[/c] and [c]printf[/c].

 axn 2020-05-27 09:07

[QUOTE=kruoli;546570]Unfortunately, that does not invert the order in a line. I'd propose:
[code]grep has results.txt | cut -d' ' -f3,7 | sort | uniq | sed 's/^\([^ ][^ ]*\) \([^ ][^ ]*\)/\2 | \1/'[/code]
(I'd be using the "c" tag but that gave weird formatting, how can I escape square brackets?)

The result seems a bit chaotic, because the first column has no constant size. One could solve that using e.g. [c]xargs[/c] and [c]printf[/c].[/QUOTE]

This works! I managed to simplify a bit (got rid of beginning of line ^, and aa* became a+, [^ ] replaced with just .):
[CODE]grep has results.txt | cut -d' ' -f3,7 | sort | uniq | sed 's/\(.\+\) \(.\+\)/\2 | \1/'[/CODE]

 kruoli 2020-05-27 12:45

Pretty-printing version

This will pad the first column with whitespaces according to the largest factor.
[code]grep has results.txt | cut -d' ' -f3,7 | sort | uniq | sed 's/\(.\+\) \(.\+\)/\2 | \1/' | xargs -n 3 printf "%-\$(grep has results.txt | cut -d' ' -f7 | sort -n | tail -n1 | wc -m)s%s %s\n"[/code]

 axn 2020-05-29 18:08

168k-169k

[CODE]11913612882321568547 | 2^168067+1
529440290127209472457 | 2^168067+1
1095097862515757003 | 2^168083+1
112935917317127940619 | 2^168127+1
4348048176533623755059 | 2^168143+1
2669252530662018811 | 2^168151+1
27792700442532935027 | 2^168227+1
64041221214314071751243929 | 2^168227+1
529892890207167563 | 2^168247+1
4425374800979048923 | 2^168277+1
14325653049315486910579 | 2^168293+1
2997939649728149563 | 2^168293+1
120639429230097257 | 2^168541+1
37532429255854149795803 | 2^168673+1
676791877255029515264648017 | 2^168673+1
378682747448705237233 | 2^168697+1
82977879931601274913123 | 2^168697+1
21255899961329433168529 | 2^168719+1
842175077092807406188231297 | 2^168851+1
7472963070582532153 | 2^168887+1
33596203202578831931 | 2^168893+1
3270063071930998012057 | 2^168937+1
4894996582062418923192889 | 2^168937+1
26073786380747794529 | 2^168991+1[/CODE]

 axn 2020-06-06 18:00

169k-170k

[CODE]44856314740724644440691 | 2^169003+1
1925201732092749571 | 2^169009+1
94368832916454704347 | 2^169079+1
87684887261795762161 | 2^169097+1
183456782470169147 | 2^169111+1
1490003561800395241 | 2^169159+1
1053354454136079249923 | 2^169199+1
367766285466743854964059 | 2^169217+1
5186030098076417562581153 | 2^169259+1
914654439736903821467 | 2^169283+1
989155624053751603534433 | 2^169319+1
186771538661686651 | 2^169321+1
3119055101114907089347 | 2^169339+1
959077436706574013921 | 2^169369+1
79748999410631609 | 2^169399+1
185751017074171142849 | 2^169489+1
16084642862163939377 | 2^169493+1
9512077193672370089 | 2^169607+1
391028789881789826953 | 2^169633+1
416382983843176379 | 2^169649+1
6040160599364897513 | 2^169657+1
160341441169662252881 | 2^169661+1
255247046465761843 | 2^169661+1
8524892844823104697 | 2^169661+1
4691777856179954170826347 | 2^169681+1
3631424494603600973017 | 2^169733+1
670137019689443135422427 | 2^169733+1
74845543182139969 | 2^169769+1
3197926054643388667 | 2^169823+1
77655479744230102067 | 2^169831+1
548564368651295961667 | 2^169859+1
280958293932157433 | 2^169889+1
440207187036120003121 | 2^169891+1
5844837817105165837481 | 2^169919+1
8026265411166975992634907 | 2^169951+1[/CODE]

 axn 2020-06-14 07:40

170k-171k

[CODE]78687184581006924353 | 2^170099+1
125817485201772947017 | 2^170197+1
151570732651386001198210873 | 2^170197+1
20515040297071876744236067 | 2^170207+1
10452892006278490843 | 2^170213+1
2824899324083571353 | 2^170239+1
1003531898087553333857191987 | 2^170243+1
10622459973799052581771 | 2^170279+1
267387692724736297033 | 2^170347+1
727592720736546283 | 2^170347+1
1109686283526930236154063773761 | 2^170351+1
1512356698561622219 | 2^170383+1
4296157942942721139491 | 2^170413+1
408321915792521359645427 | 2^170537+1
3476666510469113603 | 2^170557+1
35973057858957449231179 | 2^170557+1
170570248519149368221713763 | 2^170579+1
149061598401302634449 | 2^170633+1
1024813767061873769 | 2^170641+1
3588946352907031579451 | 2^170647+1
148435094291801877163 | 2^170749+1
549751911255936863897779 | 2^170773+1
48546829832737362409 | 2^170777+1
14075338770064082417 | 2^170809+1
3981585790303114387 | 2^170843+1
698787940504627889 | 2^170887+1
10072617257080410392881 | 2^170899+1
450720545518162130973491 | 2^170921+1
8692844142566601361445369 | 2^170957+1
96347529026468459 | 2^170957+1[/CODE]

 pinhodecarlos 2020-06-14 12:38

Wagstaff Trial factoring

Would like to donate the GPU for the cause if there’s a GPU factoring client available
but only to 70/71 bits. Higher will struggle.

 lalera 2020-06-14 18:40

hi,
why only to 70/71 bit ?
what gpu do you have ?

you need a nvidia gpu (a turing card would be nice because of the high speed)

mfaktc v0.21
the extra version for wagstaff
if you are using windows
mfaktc-win-64.Wagstaff.exe
if you are using linux
you have to compile it by yourself

 pinhodecarlos 2020-06-14 18:52

Where can I find here mfaktc-win-64.Wagstaff.exe and thread to reserve some ranges to trial factoring please?

 lalera 2020-06-14 19:17

1 Attachment(s)
[QUOTE=pinhodecarlos;547994]Where can I find here mfaktc-win-64.Wagstaff.exe and thread to reserve some ranges to trial factoring please?[/QUOTE]
hi,

[url]https://www.mersenneforum.org/mfaktc/mfaktc-0.21/mfaktc-0.21.win.cuda100.zip[/url]
[url]https://www.mersenneforum.org/mfaktc/mfaktc-0.21/mfaktc-0.21.win.cuda100.extra-versions.zip[/url]
or try the attachment

for reserving a range you can ask GP2
or you can take a look at my webpage
[url]http://deep.alotspace.com[/url]

 axn 2020-06-21 16:45

171k-172k

[CODE]1288600021986622807337 | 2^171029+1
1227343802788662547 | 2^171043+1
269730882322569323 | 2^171043+1
9700307471917948619 | 2^171049+1
37340861716226539924499 | 2^171077+1
4607101955345040381521 | 2^171079+1
170647905230592067 | 2^171091+1
142542879274957867 | 2^171103+1
6328541067404256310889 | 2^171233+1
51933855928896405066067 | 2^171253+1
17132000479867003566344051 | 2^171299+1
52451336392561256009 | 2^171329+1
613720095402994427 | 2^171341+1
2567694022366644641 | 2^171383+1
289603353439692571 | 2^171383+1
232897985302127723077321 | 2^171481+1
8055623832685117357681 | 2^171553+1
13430828887872717001 | 2^171553+1
87815019241808935027649 | 2^171559+1
87815019241808935027649 | 2^171559+1
77797647559678489 | 2^171617+1
1677594937986440711021123 | 2^171637+1
22212012019445170252553 | 2^171653+1
742505665606997849 | 2^171697+1
37995334677173500214179 | 2^171761+1
10254120346221399889 | 2^171761+1
3092923386906191068409 | 2^171863+1
62250948094549731667739 | 2^171929+1[/CODE]

 axn 2020-06-30 17:32

172k-173k

[CODE]61299296941823278841 | 2^172127+1
2988390976868813213168483137 | 2^172147+1
882829503352170347 | 2^172157+1
2553070700830370125387 | 2^172213+1
5019859203930311747 | 2^172217+1
10983286262176604233339 | 2^172219+1
586576014023572168294795035372683 | 2^172259+1
2533435488579846457 | 2^172421+1
15692404520292836563 | 2^172423+1
15836328645282109108691 | 2^172423+1
38953061322170095259 | 2^172423+1
762883922787675785377 | 2^172439+1
2451074613179607023747 | 2^172541+1
254490172204782071009057 | 2^172541+1
57622885393500236908379 | 2^172709+1
149677290522096577 | 2^172741+1
886232463682728902599217 | 2^172741+1
1193818054154262721619 | 2^172759+1
570439960397394673 | 2^172787+1
14503988829142669184747 | 2^172849+1
45443824406902104721 | 2^172877+1
17538281682126933113 | 2^172883+1
1876342676190189601 | 2^172969+1
27861793614533197285691 | 2^172981+1
959610653184668561 | 2^172999+1[/CODE]

 axn 2020-07-10 14:55

173k-174k

[CODE]30095377149881164242977 | 2^173039+1
80887278129032443193 | 2^173039+1
62613874186436759401 | 2^173053+1
16193135987820900177889 | 2^173099+1
1849714334063272667 | 2^173137+1
8637705677882220651105803 | 2^173141+1
24734790303914704577 | 2^173177+1
8697226048549936026572537 | 2^173249+1
426338847661489183891 | 2^173291+1
25154670630320653317803 | 2^173309+1
439300460166363655723 | 2^173357+1
497166004466405420281 | 2^173431+1
13566523918637079972523 | 2^173473+1
1743095620835488331 | 2^173501+1
6611662867049898353 | 2^173531+1
246069451644703619 | 2^173573+1
139642531910822062572617 | 2^173599+1
2815056030439017377 | 2^173647+1
8817068588351378609 | 2^173647+1
1070628769957916971 | 2^173651+1
4481840450850650708539 | 2^173651+1
549356261497928305257619 | 2^173729+1
266735535271817144369 | 2^173773+1
4438126815510481719049 | 2^173851+1
342532029587265333070643 | 2^173861+1
1093662802601769556483 | 2^173933+1[/CODE]

 axn 2020-07-19 02:43

174k-175k

[CODE]2^174019+1 = 139884027876484352051
2^174071+1 = 44518939632067399224494963
2^174079+1 = 1744283014767311171
2^174091+1 = 239099739246033783833
2^174121+1 = 2061987784660352201
2^174121+1 = 41209054170565291499
2^174121+1 = 519135946954279926694361
2^174241+1 = 68193298700834772529
2^174263+1 = 21039738631610712329
2^174331+1 = 183892394619296611374107
2^174389+1 = 4157369816230367939273
2^174413+1 = 390065001637342937
2^174467+1 = 12660295483629083137
2^174469+1 = 397275483480245977
2^174527+1 = 68747800876563865241
2^174533+1 = 42314571047016767393
2^174533+1 = 525707694957344436570841
2^174599+1 = 29687435414896724888153
2^174617+1 = 1585319760923323437968867
2^174631+1 = 22053407107724003377
2^174631+1 = 97656018779019338030689
2^174649+1 = 10486215038367976169530267
2^174679+1 = 6401211207422989619
2^174721+1 = 32710012567330998041
2^174737+1 = 8111859499242515790827
2^174761+1 = 1512684761218323793
2^174763+1 = 13256772483172736900801
2^174893+1 = 182983061772409057
2^174901+1 = 218884513017219704329
2^174901+1 = 21953717242339779717793969
2^174917+1 = 16481807573589697127756593
2^174943+1 = 1785614526689884096472267
2^174991+1 = 112489448403901784849[/CODE]

 axn 2020-07-22 01:48

(2^175039+1)/3 = 15484028432318997071449 . PRP52670

 paulunderwood 2020-07-22 02:51

[QUOTE=axn;551243](2^175039+1)/3 = 15484028432318997071449 . PRP52670[/QUOTE]

Congrats!

[CODE]time echo "print((2^175039+1)/3/15484028432318997071449)" | gp -q | ./lucasPRP - 1 2 175039 1
Lucas testing on x^2 - 3*x + 1 ...
Is Lucas PRP!

real 0m21.559s
user 0m21.548s
sys 0m0.037s
[/CODE]

:toot:

 kruoli 2020-07-22 08:34

[QUOTE=axn;551243](2^175039+1)/3 = 15484028432318997071449 . PRP52670[/QUOTE]

Are you doing a quick PRP on all co-factors of Wagstaff numbers you found a factor for? :smile:

 axn 2020-07-22 11:43

[QUOTE=kruoli;551265]Are you doing a quick PRP on all co-factors of Wagstaff numbers you found a factor for? :smile:[/QUOTE]

Me? No. Factordb? Yes. :smile:

Basically after submitting the factors to factodb, I also assign the cofactor to PRP worker. Then later on (maybe after a day or two), I go back and check for PRPs. Most of the time, if a PRP appears, it will be a false positive (side effect of base 2 numbers), but once in a while you hit paydirt.

 axn 2020-07-28 16:58

175k-176k

[CODE]2^175039+1 = 15484028432318997071449
2^175129+1 = 2888518630291839590281
2^175261+1 = 2848252779458437457
2^175493+1 = 325457568819025683667387
2^175493+1 = 75725050851772673224508113465282811
2^175523+1 = 4283313220014735553
2^175543+1 = 83055869146001832337
2^175573+1 = 10392142129096543267
2^175633+1 = 6273218107006677049
2^175649+1 = 49084218008288458811850467
2^175649+1 = 645535341211083611
2^175691+1 = 132484607506425353
2^175691+1 = 269574735909669667
2^175699+1 = 26167924670468650427
2^175723+1 = 61575480684464985787
2^175727+1 = 785997540666154507
2^175753+1 = 7731764578034601953
2^175757+1 = 1123852857900509344682251
2^175837+1 = 1121247319650153811
2^175853+1 = 657022808412322753
2^175919+1 = 729514846734948937385267
2^175937+1 = 259931622699811697
2^175961+1 = 2695526515777772705531[/CODE]

 axn 2020-08-09 03:02

176k-177k

[CODE]2^176021+1 = 33983817171714707083
2^176047+1 = 147239857768207753
2^176081+1 = 8800538544431775377603
2^176087+1 = 10673216986920486596130931
2^176089+1 = 203380380311264969
2^176161+1 = 9723704741388341107
2^176201+1 = 27491685841627566649
2^176207+1 = 3869296109723408099
2^176261+1 = 187542166806392569
2^176299+1 = 19104796597507146979
2^176317+1 = 1191026342830545043
2^176327+1 = 508847691812530601
2^176357+1 = 10524189435405497209
2^176383+1 = 118823506207350331
2^176389+1 = 2993340838520741603
2^176389+1 = 373012825035360673
2^176413+1 = 563822987166606017
2^176417+1 = 27436570076656790761
2^176459+1 = 846990580573167409403
2^176489+1 = 1569322481666863652914057
2^176489+1 = 323781613479405623777
2^176497+1 = 15267400915306195795753
2^176503+1 = 337412815219251677384203
2^176507+1 = 489881972761660441
2^176549+1 = 185924456695796251165101931
2^176599+1 = 1969046788413051419
2^176609+1 = 3286023352137291379
2^176609+1 = 501950353784362009
2^176651+1 = 3962235072334733623566827
2^176711+1 = 191554838438043601
2^176791+1 = 5973166876161887729
2^176791+1 = 65059246475249643377068042073
2^176797+1 = 2432579326117556257
2^176807+1 = 1464333485161559449
2^176849+1 = 31353746691641494489
2^176857+1 = 1038277119771813747563
2^176903+1 = 307517101193555459
2^176921+1 = 16880839838412406057
2^176927+1 = 1856505474870419809
2^176933+1 = 49912940927217686411
2^176977+1 = 25350011810238691178501054899[/CODE]

 axn 2020-08-18 02:55

177k-178k

[CODE]2^177011+1 = 106247300131063066483
2^177013+1 = 465958696873229803
2^177019+1 = 2315470461171687702587
2^177043+1 = 164772305082767428151107
2^177101+1 = 2389566866428137169
2^177109+1 = 53573357192080645370949427
2^177127+1 = 590220157859678557459
2^177173+1 = 2421653898116788248643
2^177173+1 = 4805829220950171857
2^177223+1 = 211063619216889066020401
2^177257+1 = 2109880828526050417446899
2^177269+1 = 4570419998978742073457
2^177283+1 = 331169775131504861233379
2^177347+1 = 344718951328415992538380243
2^177409+1 = 9099989993871755171
2^177421+1 = 28433728920056556241
2^177487+1 = 1056686974944848507539
2^177487+1 = 17877728635596061093361
2^177601+1 = 116400718148051266860659
2^177679+1 = 10760909630573908115868611243
2^177739+1 = 1339166159723971171
2^177787+1 = 172787530646972263961
2^177787+1 = 30707031761418538911582163
2^177791+1 = 468216429977685068490011
2^177811+1 = 106312477509055603
2^177823+1 = 152013173424859000869133867
2^177883+1 = 108355633305923886701120722617888753521
2^177887+1 = 116753900596588338976418579
2^177907+1 = 4949975740132726169017
2^177913+1 = 1602295770888160037642401
2^177917+1 = 4629986408240033899
2^177979+1 = 359585350919183970026444406929[/CODE]

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