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Message boards : Project Staging Area : Wieferich - it has been a while

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Profile Toshio Yamaguchi
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Joined: 19 May 11
Posts: 134
ID: 99209
Credit: 665,512
RAC: 0
321 LLR Bronze: Earned 10,000 credits (16,424)PPS LLR Bronze: Earned 10,000 credits (10,232)SR5 LLR Bronze: Earned 10,000 credits (10,448)TRP LLR Bronze: Earned 10,000 credits (24,275)Woodall LLR Bronze: Earned 10,000 credits (19,632)PPS Sieve Bronze: Earned 10,000 credits (89,027)TRP Sieve (suspended) Bronze: Earned 10,000 credits (20,665)PSA Silver: Earned 100,000 credits (469,144)
Message 55340 - Posted: 10 Jun 2012 | 13:48:42 UTC

Congratulations to K Lewis for finding 19030795636403797. That's the first near Wieferich with |A| < 100 in a while and the first with |A| < 100 above 3e15 that had not already been found by Dorais and Klyve beforehand. Nice.

Profile Roger
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Joined: 27 Nov 11
Posts: 1137
ID: 120786
Credit: 267,278,751
RAC: 8,580
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 60110 - Posted: 5 Dec 2012 | 5:23:25 UTC - in response to Message 55340.

Yay, I got a Wieferich near find!
69397046751123461 (-1 -173 p). That was the hardest near find to date, requiring 37,353 tests.
The number of tests required till the next near find loosely follows an exponential curve.
Now I can relax for the PRPNet 27 Challenge.

____________

rogue
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Joined: 8 Sep 07
Posts: 1200
ID: 12001
Credit: 18,565,548
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PPS LLR Bronze: Earned 10,000 credits (31,229)PSA Jade: Earned 10,000,000 credits (18,533,435)
Message 60711 - Posted: 22 Dec 2012 | 17:21:20 UTC

As many of you are probably not aware, Richard Crandall got me involved with the Wieferich search a number of years ago. Working with him led to the creation of a Wieferich search I did a few years ago and more recently prompted me to learn about OpenCL and write wwwwcl. It was his hope that another Wieferich prime would be found in his lifetime. Sadly, that didn't happen as he died on Thursday. He was very well known in the mathematics community and it was an algorithm of his, the Discrete Weight Transform, that is behind most prime searches today.

In his memory, I propose that everyone dedicate some CPU and/or GPU power to the Wieferich search for a few days. Maybe we'll get lucky.

Profile Crun-chiProject donor
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Joined: 25 Nov 09
Posts: 2993
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Credit: 58,227,698
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Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Turquoise: Earned 5,000,000 credits (7,173,525)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,855,975)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)WW Silver: Earned 100,000 credits (116,000)GFN Sapphire: Earned 20,000,000 credits (23,334,026)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 60712 - Posted: 22 Dec 2012 | 17:26:31 UTC - in response to Message 60711.

R.I.P Richard Crandall :(
____________
314187728^131072+1 GENERALIZED FERMAT :)
93*10^1029523-1 REPDIGIT PRIME
31*332^367560+1 CRUS PRIME
Proud member of team Aggie The Pew. Go Aggie!

Profile Michael GoetzProject donor
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Posts: 13434
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Credit: 232,451,827
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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (3,582,762)ESP LLR Turquoise: Earned 5,000,000 credits (5,021,269)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Jade: Earned 10,000,000 credits (16,008,485)PSP LLR Turquoise: Earned 5,000,000 credits (5,197,957)SoB LLR Sapphire: Earned 20,000,000 credits (34,291,181)SR5 LLR Jade: Earned 10,000,000 credits (10,007,110)SGS LLR Ruby: Earned 2,000,000 credits (2,292,734)TRP LLR Turquoise: Earned 5,000,000 credits (5,084,329)Woodall LLR Ruby: Earned 2,000,000 credits (2,887,264)321 Sieve (suspended) Jade: Earned 10,000,000 credits (10,061,196)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (22,885,121)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,118,303)WW Silver: Earned 100,000 credits (184,000)GFN Emerald: Earned 50,000,000 credits (75,106,275)PSA Jade: Earned 10,000,000 credits (12,445,029)
Message 60713 - Posted: 22 Dec 2012 | 18:07:21 UTC

It is extremely sad to hear of his passing, and I'd like to offer my condolences to his family and friends. The world is a lesser place now.

____________
My lucky number is 75898524288+1

Profile Gary Craig
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Joined: 30 Dec 09
Posts: 3213
ID: 52890
Credit: 1,005,618,748
RAC: 0
Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,893,273)Cullen LLR Ruby: Earned 2,000,000 credits (2,440,687)ESP LLR Turquoise: Earned 5,000,000 credits (5,738,876)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (6,292,626)PPS LLR Turquoise: Earned 5,000,000 credits (9,648,951)PSP LLR Turquoise: Earned 5,000,000 credits (5,653,927)SoB LLR Jade: Earned 10,000,000 credits (10,558,341)SR5 LLR Turquoise: Earned 5,000,000 credits (5,748,705)SGS LLR Ruby: Earned 2,000,000 credits (3,335,713)TRP LLR Jade: Earned 10,000,000 credits (12,602,818)Woodall LLR Ruby: Earned 2,000,000 credits (2,282,622)321 Sieve (suspended) Gold: Earned 500,000 credits (740,566)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (59,788,598)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,143,068)PPS Sieve Double Gold: Earned 500,000,000 credits (524,673,938)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,130,821)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,074,710)AP 26/27 Sapphire: Earned 20,000,000 credits (43,842,888)GFN Double Silver: Earned 200,000,000 credits (224,648,943)PSA Emerald: Earned 50,000,000 credits (62,378,755)
Message 60718 - Posted: 23 Dec 2012 | 7:21:19 UTC

Thank you Mark for sending along the news, sad though it may be.

--Gary

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Joined: 15 Aug 05
Posts: 1887
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RAC: 1,089,998
Discovered 7 mega primesEliminated 4 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes largest primeFound 4 primes in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de PrimesFound 1 prime in the 2019 Tour de Primes Mountain StageFound 1 prime in the 2020 Tour de Primes321 LLR Emerald: Earned 50,000,000 credits (91,304,446)Cullen LLR Emerald: Earned 50,000,000 credits (58,765,989)ESP LLR Emerald: Earned 50,000,000 credits (50,853,190)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,309,119)PPS LLR Double Bronze: Earned 100,000,000 credits (122,476,468)PSP LLR Emerald: Earned 50,000,000 credits (50,563,867)SoB LLR Double Bronze: Earned 100,000,000 credits (101,502,109)SR5 LLR Double Bronze: Earned 100,000,000 credits (101,883,529)SGS LLR Emerald: Earned 50,000,000 credits (53,154,727)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Double Bronze: Earned 100,000,000 credits (100,338,924)Woodall LLR Emerald: Earned 50,000,000 credits (50,956,094)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (115,948,450)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (513,057,580)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Double Silver: Earned 200,000,000 credits (232,724,773)WW Gold: Earned 500,000 credits (792,000)GFN Double Gold: Earned 500,000,000 credits (745,852,196)PSA Double Gold: Earned 500,000,000 credits (535,232,795)
Message 61615 - Posted: 12 Jan 2013 | 19:06:16 UTC
Last modified: 11 Jun 2013 | 10:16:37 UTC

Out of curiosity, there is a mock-up graph of Near Wieferich founds so far.

http://s2.postimage.org/upgl0qant/Wieferich.png


____________
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Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

rogue
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Joined: 8 Sep 07
Posts: 1200
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Credit: 18,565,548
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PPS LLR Bronze: Earned 10,000 credits (31,229)PSA Jade: Earned 10,000,000 credits (18,533,435)
Message 61620 - Posted: 12 Jan 2013 | 22:40:55 UTC - in response to Message 61615.

Our of curiosity, there is a mock-up graph of Near Weiferich founds so far.

http://s2.postimage.org/upgl0qant/Wieferich.png



That's interesting, but I wonder how it would look if the x axis were logarithmic.

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Joined: 15 Aug 05
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Discovered 7 mega primesEliminated 4 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes largest primeFound 4 primes in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de PrimesFound 1 prime in the 2019 Tour de Primes Mountain StageFound 1 prime in the 2020 Tour de Primes321 LLR Emerald: Earned 50,000,000 credits (91,304,446)Cullen LLR Emerald: Earned 50,000,000 credits (58,765,989)ESP LLR Emerald: Earned 50,000,000 credits (50,853,190)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,309,119)PPS LLR Double Bronze: Earned 100,000,000 credits (122,476,468)PSP LLR Emerald: Earned 50,000,000 credits (50,563,867)SoB LLR Double Bronze: Earned 100,000,000 credits (101,502,109)SR5 LLR Double Bronze: Earned 100,000,000 credits (101,883,529)SGS LLR Emerald: Earned 50,000,000 credits (53,154,727)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Double Bronze: Earned 100,000,000 credits (100,338,924)Woodall LLR Emerald: Earned 50,000,000 credits (50,956,094)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (115,948,450)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (513,057,580)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Double Silver: Earned 200,000,000 credits (232,724,773)WW Gold: Earned 500,000 credits (792,000)GFN Double Gold: Earned 500,000,000 credits (745,852,196)PSA Double Gold: Earned 500,000,000 credits (535,232,795)
Message 61630 - Posted: 13 Jan 2013 | 7:43:17 UTC - in response to Message 61620.
Last modified: 13 Jan 2013 | 14:56:16 UTC

That's interesting, but I wonder how it would look if the x axis were logarithmic.


Hope I got it right... http://postimage.org/image/nzdxprg7h/


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Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

Brook HarsteProject donor
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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 61717 - Posted: 16 Jan 2013 | 3:07:29 UTC
Last modified: 16 Jan 2013 | 3:14:56 UTC

I got one today! My last one was in July. :0
82684879689553451 (-1 -458 p)

But look at this one found today,
MiHost 82687771042557349 (-1 -10 p)
WOW! Very close!
____________

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Joined: 15 Aug 05
Posts: 1887
ID: 352
Credit: 3,070,856,729
RAC: 1,089,998
Discovered 7 mega primesEliminated 4 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes largest primeFound 4 primes in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de PrimesFound 1 prime in the 2019 Tour de Primes Mountain StageFound 1 prime in the 2020 Tour de Primes321 LLR Emerald: Earned 50,000,000 credits (91,304,446)Cullen LLR Emerald: Earned 50,000,000 credits (58,765,989)ESP LLR Emerald: Earned 50,000,000 credits (50,853,190)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,309,119)PPS LLR Double Bronze: Earned 100,000,000 credits (122,476,468)PSP LLR Emerald: Earned 50,000,000 credits (50,563,867)SoB LLR Double Bronze: Earned 100,000,000 credits (101,502,109)SR5 LLR Double Bronze: Earned 100,000,000 credits (101,883,529)SGS LLR Emerald: Earned 50,000,000 credits (53,154,727)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Double Bronze: Earned 100,000,000 credits (100,338,924)Woodall LLR Emerald: Earned 50,000,000 credits (50,956,094)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (115,948,450)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (513,057,580)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Double Silver: Earned 200,000,000 credits (232,724,773)WW Gold: Earned 500,000 credits (792,000)GFN Double Gold: Earned 500,000,000 credits (745,852,196)PSA Double Gold: Earned 500,000,000 credits (535,232,795)
Message 61722 - Posted: 16 Jan 2013 | 7:46:25 UTC - in response to Message 61717.

But look at this one found today,
MiHost 82687771042557349 (-1 -10 p)
WOW! Very close!


I think that's nearest one we have found so far!

____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

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Joined: 5 Feb 08
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Found 1 prime in the 2019 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,310,491)Cullen LLR Amethyst: Earned 1,000,000 credits (1,086,094)ESP LLR Amethyst: Earned 1,000,000 credits (1,875,010)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,216,209)PPS LLR Turquoise: Earned 5,000,000 credits (5,212,863)PSP LLR Amethyst: Earned 1,000,000 credits (1,323,642)SoB LLR Turquoise: Earned 5,000,000 credits (7,603,584)SR5 LLR Amethyst: Earned 1,000,000 credits (1,891,772)SGS LLR Amethyst: Earned 1,000,000 credits (1,163,706)TRP LLR Ruby: Earned 2,000,000 credits (3,832,495)Woodall LLR Amethyst: Earned 1,000,000 credits (1,506,073)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,432,077)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,967,439)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,137,451)PPS Sieve Double Silver: Earned 200,000,000 credits (269,379,670)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (627,444)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (3,956,401)AP 26/27 Jade: Earned 10,000,000 credits (15,856,233)WW Silver: Earned 100,000 credits (496,000)GFN Emerald: Earned 50,000,000 credits (64,937,531)PSA Emerald: Earned 50,000,000 credits (87,901,787)
Message 61736 - Posted: 16 Jan 2013 | 16:48:27 UTC - in response to Message 61722.

But look at this one found today,
MiHost 82687771042557349 (-1 -10 p)
WOW! Very close!


I think that's nearest one we have found so far!

Yes

according to my list (sorted by value) the formerly nearest were
user team client value date reported Tarmo_Ilves Aggie_The_Pew server3 3723113065138349 (-1 +18 p) Saturday 31st of December 2011 04:31:52 PM JAMC My_Way 2 5131427559624857 (+1 -18 p) Tuesday 03rd of January 2012 10:51:51 PM

____________
Sysadm@Nbg
my current lucky number: 3749*2^1555697+1
PSA-PRPNet-Stats-URL: http://u-g-f.de/PRPNet/

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Credit: 5,200,580,966
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Discovered 2 mega primesFound 2 primes in the 2018 Tour de PrimesFound 2 primes in the 2019 Tour de PrimesFound 12 primes in the 2020 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,244,909)Cullen LLR Turquoise: Earned 5,000,000 credits (8,336,430)ESP LLR Turquoise: Earned 5,000,000 credits (5,174,327)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,028,260)PPS LLR Emerald: Earned 50,000,000 credits (59,236,744)PSP LLR Turquoise: Earned 5,000,000 credits (5,151,448)SoB LLR Turquoise: Earned 5,000,000 credits (5,014,268)SR5 LLR Jade: Earned 10,000,000 credits (14,871,275)SGS LLR Turquoise: Earned 5,000,000 credits (7,860,522)TRP LLR Jade: Earned 10,000,000 credits (11,130,742)Woodall LLR Turquoise: Earned 5,000,000 credits (5,419,909)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (101,538,236)Cullen/Woodall Sieve (suspended) Double Bronze: Earned 100,000,000 credits (127,922,665)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (30,984,158)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,840,173,136)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,134,964)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (7,013,696)AP 26/27 Double Silver: Earned 200,000,000 credits (276,723,135)WW Turquoise: Earned 5,000,000 credits (6,856,000)GFN Double Silver: Earned 200,000,000 credits (293,113,761)PSA Double Amethyst: Earned 1,000,000,000 credits (1,370,700,486)
Message 61740 - Posted: 16 Jan 2013 | 17:12:16 UTC - in response to Message 61717.

I got one today! My last one was in July. :0
82684879689553451 (-1 -458 p)

But look at this one found today,
MiHost 82687771042557349 (-1 -10 p)
WOW! Very close!


Just saw this post.. CongRATS !

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RAC: 1,089,998
Discovered 7 mega primesEliminated 4 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes largest primeFound 4 primes in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de PrimesFound 1 prime in the 2019 Tour de Primes Mountain StageFound 1 prime in the 2020 Tour de Primes321 LLR Emerald: Earned 50,000,000 credits (91,304,446)Cullen LLR Emerald: Earned 50,000,000 credits (58,765,989)ESP LLR Emerald: Earned 50,000,000 credits (50,853,190)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,309,119)PPS LLR Double Bronze: Earned 100,000,000 credits (122,476,468)PSP LLR Emerald: Earned 50,000,000 credits (50,563,867)SoB LLR Double Bronze: Earned 100,000,000 credits (101,502,109)SR5 LLR Double Bronze: Earned 100,000,000 credits (101,883,529)SGS LLR Emerald: Earned 50,000,000 credits (53,154,727)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Double Bronze: Earned 100,000,000 credits (100,338,924)Woodall LLR Emerald: Earned 50,000,000 credits (50,956,094)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (115,948,450)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (513,057,580)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Double Silver: Earned 200,000,000 credits (232,724,773)WW Gold: Earned 500,000 credits (792,000)GFN Double Gold: Earned 500,000,000 credits (745,852,196)PSA Double Gold: Earned 500,000,000 credits (535,232,795)
Message 61747 - Posted: 16 Jan 2013 | 20:27:12 UTC - in response to Message 61736.

according to my list (sorted by value) the formerly nearest were...

Can you make link to this page somewhere? Or have I missed it before? It would have been easier to make graph if I knew this link.

http://u-g-f.de/PRPNet/help.html may be suitable.

____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

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Found 1 prime in the 2019 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,310,491)Cullen LLR Amethyst: Earned 1,000,000 credits (1,086,094)ESP LLR Amethyst: Earned 1,000,000 credits (1,875,010)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,216,209)PPS LLR Turquoise: Earned 5,000,000 credits (5,212,863)PSP LLR Amethyst: Earned 1,000,000 credits (1,323,642)SoB LLR Turquoise: Earned 5,000,000 credits (7,603,584)SR5 LLR Amethyst: Earned 1,000,000 credits (1,891,772)SGS LLR Amethyst: Earned 1,000,000 credits (1,163,706)TRP LLR Ruby: Earned 2,000,000 credits (3,832,495)Woodall LLR Amethyst: Earned 1,000,000 credits (1,506,073)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,432,077)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,967,439)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,137,451)PPS Sieve Double Silver: Earned 200,000,000 credits (269,379,670)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (627,444)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (3,956,401)AP 26/27 Jade: Earned 10,000,000 credits (15,856,233)WW Silver: Earned 100,000 credits (496,000)GFN Emerald: Earned 50,000,000 credits (64,937,531)PSA Emerald: Earned 50,000,000 credits (87,901,787)
Message 61757 - Posted: 17 Jan 2013 | 7:09:34 UTC - in response to Message 61747.

according to my list (sorted by value) the formerly nearest were...

Can you make link to this page somewhere? Or have I missed it before? It would have been easier to make graph if I knew this link.

http://u-g-f.de/PRPNet/help.html may be suitable.

Link is there:
starting page http://u-g-f.de/PRPNet/ row "WFS" column "hits"
named "findlist" (equivalent to the primelist at prime searches)
____________
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my current lucky number: 3749*2^1555697+1
PSA-PRPNet-Stats-URL: http://u-g-f.de/PRPNet/

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Joined: 15 Aug 05
Posts: 1887
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Discovered 7 mega primesEliminated 4 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes largest primeFound 4 primes in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de PrimesFound 1 prime in the 2019 Tour de Primes Mountain StageFound 1 prime in the 2020 Tour de Primes321 LLR Emerald: Earned 50,000,000 credits (91,304,446)Cullen LLR Emerald: Earned 50,000,000 credits (58,765,989)ESP LLR Emerald: Earned 50,000,000 credits (50,853,190)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,309,119)PPS LLR Double Bronze: Earned 100,000,000 credits (122,476,468)PSP LLR Emerald: Earned 50,000,000 credits (50,563,867)SoB LLR Double Bronze: Earned 100,000,000 credits (101,502,109)SR5 LLR Double Bronze: Earned 100,000,000 credits (101,883,529)SGS LLR Emerald: Earned 50,000,000 credits (53,154,727)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Double Bronze: Earned 100,000,000 credits (100,338,924)Woodall LLR Emerald: Earned 50,000,000 credits (50,956,094)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (115,948,450)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (513,057,580)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Double Silver: Earned 200,000,000 credits (232,724,773)WW Gold: Earned 500,000 credits (792,000)GFN Double Gold: Earned 500,000,000 credits (745,852,196)PSA Double Gold: Earned 500,000,000 credits (535,232,795)
Message 61799 - Posted: 18 Jan 2013 | 9:11:09 UTC - in response to Message 61757.

Link is there:
starting page http://u-g-f.de/PRPNet/ row "WFS" column "hits"
named "findlist" (equivalent to the primelist at prime searches)

Thanks, I've missed that one before.

Last found is encouraging.
We are doing >100k tests a month and should clear current range up to 100e15 before end of February.
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Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

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Joined: 30 Nov 08
Posts: 1345
ID: 32401
Credit: 805,483,198
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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 62035 - Posted: 27 Jan 2013 | 17:43:53 UTC

Nice sub 100 find Scott

Scott_Brown Duke_University GT-640 90845186086414511 (+1 -77 p) Sunday 27th of January 2013 03:22:58 PM

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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 26 mega primesEliminated 7 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 2 Fermat divisors2012 Tour de Primes highest prime count2012 Tour de Primes most Mountain Stage primes2015 Tour de Primes highest prime count2016 Tour de Primes highest prime countFound 23 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 2 primes in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes highest prime countFound 22 primes in the 2019 Tour de Primes2020 Tour de Primes highest prime scoreFound 21 primes in the 2020 Tour de PrimesFound 4 mega primes in the 2020 Tour de Primes321 LLR Double Silver: Earned 200,000,000 credits (201,403,028)Cullen LLR Double Bronze: Earned 100,000,000 credits (128,626,022)ESP LLR Double Silver: Earned 200,000,000 credits (203,249,784)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (109,580,172)PPS LLR Double Gold: Earned 500,000,000 credits (645,585,663)PSP LLR Double Bronze: Earned 100,000,000 credits (126,982,721)SoB LLR Double Bronze: Earned 100,000,000 credits (135,747,083)SR5 LLR Double Silver: Earned 200,000,000 credits (214,194,272)SGS LLR Double Silver: Earned 200,000,000 credits (200,644,843)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Silver: Earned 200,000,000 credits (201,215,056)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,447,725)321 Sieve (suspended) Double Silver: Earned 200,000,000 credits (235,451,253)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve (suspended) Double Silver: Earned 200,000,000 credits (285,139,652)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,727,992,743)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Silver: Earned 200,000,000 credits (203,523,358)TRP Sieve (suspended) Double Silver: Earned 200,000,000 credits (201,489,157)AP 26/27 Double Silver: Earned 200,000,000 credits (385,720,907)WW Turquoise: Earned 5,000,000 credits (6,252,000)GFN Double Amethyst: Earned 1,000,000,000 credits (1,926,270,311)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 62037 - Posted: 27 Jan 2013 | 18:12:46 UTC - in response to Message 62035.

Nice sub 100 find Scott

Scott_Brown Duke_University GT-640 90845186086414511 (+1 -77 p) Sunday 27th of January 2013 03:22:58 PM


Thanks. It was a good Wieferich near find day overall! ...and a double shot for you!

Scott_Brown Duke_University GT-640 90845186086414511 (+1 -77 p) Sunday 27th of January 2013 03:22:58 PM Honza BOINC.SK Honza 90789964532564971 (-1 +570 p) Sunday 27th of January 2013 02:02:27 PM brinktastee Aggie_The_Pew eviltim 90556733200674001 (+1 -126 p) Sunday 27th of January 2013 02:57:26 AM brinktastee Aggie_The_Pew eviltim 90519940212656789 (-1 -320 p) Sunday 27th of January 2013 01:31:02 AM





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Joined: 27 Nov 11
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Credit: 267,278,751
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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 65460 - Posted: 17 May 2013 | 5:49:36 UTC - in response to Message 60110.

First time I've crunched WFS this year and after 2 days found my fourth near Wieferich!
114246519827636887 (+1 -467 p)

This is the 21st near Wieferich find this year.

Brook HarsteProject donor
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Joined: 30 Nov 08
Posts: 1345
ID: 32401
Credit: 805,483,198
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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 65478 - Posted: 17 May 2013 | 21:38:09 UTC - in response to Message 65460.

First time I've crunched WFS this year and after 2 days found my fourth near Wieferich!
114246519827636887 (+1 -467 p)

This is the 21st near Wieferich find this year.

Nice one Roger!
It's been a while for me. Hope to get one soon ;)
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Joined: 30 Nov 08
Posts: 1345
ID: 32401
Credit: 805,483,198
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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 65702 - Posted: 22 May 2013 | 13:19:08 UTC

I got one today. Pretty low too!!

WFS 115341564749415161 (+1 +34 p) Aggie_The_Pew asus-i7-950 Wednesday 22nd of May 2013 12:00:59 PM

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321 LLR Bronze: Earned 10,000 credits (16,424)PPS LLR Bronze: Earned 10,000 credits (10,232)SR5 LLR Bronze: Earned 10,000 credits (10,448)TRP LLR Bronze: Earned 10,000 credits (24,275)Woodall LLR Bronze: Earned 10,000 credits (19,632)PPS Sieve Bronze: Earned 10,000 credits (89,027)TRP Sieve (suspended) Bronze: Earned 10,000 credits (20,665)PSA Silver: Earned 100,000 credits (469,144)
Message 65726 - Posted: 22 May 2013 | 22:16:28 UTC - in response to Message 65702.

I got one today. Pretty low too!!
WFS 115341564749415161 (+1 +34 p) Aggie_The_Pew asus-i7-950 Wednesday 22nd of May 2013 12:00:59 PM


Congrats. That's one of the closest so far and the second closest above the range that had been searched by Dorais & Klyve.

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Credit: 1,005,618,748
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Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,893,273)Cullen LLR Ruby: Earned 2,000,000 credits (2,440,687)ESP LLR Turquoise: Earned 5,000,000 credits (5,738,876)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (6,292,626)PPS LLR Turquoise: Earned 5,000,000 credits (9,648,951)PSP LLR Turquoise: Earned 5,000,000 credits (5,653,927)SoB LLR Jade: Earned 10,000,000 credits (10,558,341)SR5 LLR Turquoise: Earned 5,000,000 credits (5,748,705)SGS LLR Ruby: Earned 2,000,000 credits (3,335,713)TRP LLR Jade: Earned 10,000,000 credits (12,602,818)Woodall LLR Ruby: Earned 2,000,000 credits (2,282,622)321 Sieve (suspended) Gold: Earned 500,000 credits (740,566)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (59,788,598)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,143,068)PPS Sieve Double Gold: Earned 500,000,000 credits (524,673,938)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,130,821)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,074,710)AP 26/27 Sapphire: Earned 20,000,000 credits (43,842,888)GFN Double Silver: Earned 200,000,000 credits (224,648,943)PSA Emerald: Earned 50,000,000 credits (62,378,755)
Message 65741 - Posted: 23 May 2013 | 4:46:51 UTC - in response to Message 65726.
Last modified: 23 May 2013 | 4:47:35 UTC

I got one today. Pretty low too!!
WFS 115341564749415161 (+1 +34 p) Aggie_The_Pew asus-i7-950 Wednesday 22nd of May 2013 12:00:59 PM


Congrats. That's one of the closest so far and the second closest above the range that had been searched by Dorais & Klyve.

Go AtP! (And yes, congratulations on the find).

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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 65745 - Posted: 23 May 2013 | 6:11:47 UTC - in response to Message 65702.

Congrats brinktastee on your nice near find! That's 10 for you overall. Looks like your about to overtake Scott Brown on points as well to claim 2nd place.

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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 26 mega primesEliminated 7 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 2 Fermat divisors2012 Tour de Primes highest prime count2012 Tour de Primes most Mountain Stage primes2015 Tour de Primes highest prime count2016 Tour de Primes highest prime countFound 23 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 2 primes in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes highest prime countFound 22 primes in the 2019 Tour de Primes2020 Tour de Primes highest prime scoreFound 21 primes in the 2020 Tour de PrimesFound 4 mega primes in the 2020 Tour de Primes321 LLR Double Silver: Earned 200,000,000 credits (201,403,028)Cullen LLR Double Bronze: Earned 100,000,000 credits (128,626,022)ESP LLR Double Silver: Earned 200,000,000 credits (203,249,784)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (109,580,172)PPS LLR Double Gold: Earned 500,000,000 credits (645,585,663)PSP LLR Double Bronze: Earned 100,000,000 credits (126,982,721)SoB LLR Double Bronze: Earned 100,000,000 credits (135,747,083)SR5 LLR Double Silver: Earned 200,000,000 credits (214,194,272)SGS LLR Double Silver: Earned 200,000,000 credits (200,644,843)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Silver: Earned 200,000,000 credits (201,215,056)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,447,725)321 Sieve (suspended) Double Silver: Earned 200,000,000 credits (235,451,253)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve (suspended) Double Silver: Earned 200,000,000 credits (285,139,652)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,727,992,743)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Silver: Earned 200,000,000 credits (203,523,358)TRP Sieve (suspended) Double Silver: Earned 200,000,000 credits (201,489,157)AP 26/27 Double Silver: Earned 200,000,000 credits (385,720,907)WW Turquoise: Earned 5,000,000 credits (6,252,000)GFN Double Amethyst: Earned 1,000,000,000 credits (1,926,270,311)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 67147 - Posted: 21 Jun 2013 | 15:18:05 UTC

Finally knocked rogue out of the top spot...Phew! that took a while.

Now let's find one of these very elusive primes!

Brook HarsteProject donor
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Credit: 805,483,198
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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 67153 - Posted: 21 Jun 2013 | 16:26:24 UTC - in response to Message 67147.

Finally knocked rogue out of the top spot...Phew! that took a while.

Now let's find one of these very elusive primes!


I'm STILL gunning for you Scott!
I just can't quite get to you and when I do I fall back behind.
Now I'm going on vacation and will be shutting down so I will have to try even harder to get to you when I get back. :) <evil laugh>
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Joined: 17 Oct 05
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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 26 mega primesEliminated 7 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 2 Fermat divisors2012 Tour de Primes highest prime count2012 Tour de Primes most Mountain Stage primes2015 Tour de Primes highest prime count2016 Tour de Primes highest prime countFound 23 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 2 primes in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes highest prime countFound 22 primes in the 2019 Tour de Primes2020 Tour de Primes highest prime scoreFound 21 primes in the 2020 Tour de PrimesFound 4 mega primes in the 2020 Tour de Primes321 LLR Double Silver: Earned 200,000,000 credits (201,403,028)Cullen LLR Double Bronze: Earned 100,000,000 credits (128,626,022)ESP LLR Double Silver: Earned 200,000,000 credits (203,249,784)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (109,580,172)PPS LLR Double Gold: Earned 500,000,000 credits (645,585,663)PSP LLR Double Bronze: Earned 100,000,000 credits (126,982,721)SoB LLR Double Bronze: Earned 100,000,000 credits (135,747,083)SR5 LLR Double Silver: Earned 200,000,000 credits (214,194,272)SGS LLR Double Silver: Earned 200,000,000 credits (200,644,843)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Silver: Earned 200,000,000 credits (201,215,056)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,447,725)321 Sieve (suspended) Double Silver: Earned 200,000,000 credits (235,451,253)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve (suspended) Double Silver: Earned 200,000,000 credits (285,139,652)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,727,992,743)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Silver: Earned 200,000,000 credits (203,523,358)TRP Sieve (suspended) Double Silver: Earned 200,000,000 credits (201,489,157)AP 26/27 Double Silver: Earned 200,000,000 credits (385,720,907)WW Turquoise: Earned 5,000,000 credits (6,252,000)GFN Double Amethyst: Earned 1,000,000,000 credits (1,926,270,311)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 67251 - Posted: 24 Jun 2013 | 14:08:51 UTC - in response to Message 67153.

Finally knocked rogue out of the top spot...Phew! that took a while.

Now let's find one of these very elusive primes!


I'm STILL gunning for you Scott!
I just can't quite get to you and when I do I fall back behind.
Now I'm going on vacation and will be shutting down so I will have to try even harder to get to you when I get back. :) <evil laugh>



Oh, you'll get me I think. I am moving over to Wall-Sun-Sun to catch that project back up from the application error work...and I will be on vacation in about 5 weeks, so you'll probably catch me then.

Have a good and safe vacation.

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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 67952 - Posted: 27 Jul 2013 | 23:47:43 UTC - in response to Message 67251.
Last modified: 27 Jul 2013 | 23:49:30 UTC

Yay! I got a Wieferich near find. My 5th so far.
124594134536762119 (+1 +850 p)
That one took us 39,733 tests to find. At this p level I would expect an average of one every 10,000 tests.
The biggest gap so far was 60,094 tests. The test required will only increase.
Maybe we need a message in the software telling us how close we got for each test, even if it wasn't near, so we know its working.

My record time for one Wieferich test is now 44.54 seconds! I've got the screen shot to prove it.
I can average 49 seconds per test, so about 6 days full crunching till the next near find.

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321 LLR Bronze: Earned 10,000 credits (16,424)PPS LLR Bronze: Earned 10,000 credits (10,232)SR5 LLR Bronze: Earned 10,000 credits (10,448)TRP LLR Bronze: Earned 10,000 credits (24,275)Woodall LLR Bronze: Earned 10,000 credits (19,632)PPS Sieve Bronze: Earned 10,000 credits (89,027)TRP Sieve (suspended) Bronze: Earned 10,000 credits (20,665)PSA Silver: Earned 100,000 credits (469,144)
Message 69331 - Posted: 20 Sep 2013 | 16:29:28 UTC - in response to Message 67952.
Last modified: 20 Sep 2013 | 16:32:30 UTC

Maybe we need a message in the software telling us how close we got for each test, even if it wasn't near, so we know its working.

That's already possible via the -s parameter in wwww and wwwwcl, which currently seems to be used with -s1000. I suspect that this value for -s is configured on the server side and passed to wwww as parameter when it processes a range received from the port.

Note that the value of the -s parameter corresponds to the A value in the congruence
2^((p−1)/2) ≡ ±1 + Ap (mod p^2)
That A exists for any prime p. The closeness you are asking for is thus exactly measured by the size of A. I think having the software report that value for every prime isn't particularly useful.

When p is large, A will also be quite large most of the time.

Brook HarsteProject donor
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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 78090 - Posted: 15 Jul 2014 | 3:07:22 UTC
Last modified: 15 Jul 2014 | 3:10:37 UTC

I got a near today.
145172216558999221 (-1 +26 p)
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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 78092 - Posted: 15 Jul 2014 | 5:17:22 UTC - in response to Message 78090.

I got a near today.
145172216558999221 (-1 +26 p)

Well done brinktastee! That's the 5th nearest find on PRPNet so far.

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 78099 - Posted: 15 Jul 2014 | 8:44:31 UTC - in response to Message 78092.

I got a near today.
145172216558999221 (-1 +26 p)

Well done brinktastee! That's the 5th nearest find on PRPNet so far.


If instead we use |A|/p as our measure of being "nearly" Wieferich (so calculate 26/145172216558999221 in this case), the find of yesterday appears to be the second-nearest, at 1.79e-16.

Well done indeed.

Of course one can argue that the measure |A| is more relevant.

/JeppeSN

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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 78248 - Posted: 22 Jul 2014 | 15:18:36 UTC

Grabbed another one today! :)
147348089501325541 (-1 -360 p)
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Found 1 prime in the 2019 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,310,491)Cullen LLR Amethyst: Earned 1,000,000 credits (1,086,094)ESP LLR Amethyst: Earned 1,000,000 credits (1,875,010)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,216,209)PPS LLR Turquoise: Earned 5,000,000 credits (5,212,863)PSP LLR Amethyst: Earned 1,000,000 credits (1,323,642)SoB LLR Turquoise: Earned 5,000,000 credits (7,603,584)SR5 LLR Amethyst: Earned 1,000,000 credits (1,891,772)SGS LLR Amethyst: Earned 1,000,000 credits (1,163,706)TRP LLR Ruby: Earned 2,000,000 credits (3,832,495)Woodall LLR Amethyst: Earned 1,000,000 credits (1,506,073)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,432,077)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,967,439)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,137,451)PPS Sieve Double Silver: Earned 200,000,000 credits (269,379,670)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (627,444)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (3,956,401)AP 26/27 Jade: Earned 10,000,000 credits (15,856,233)WW Silver: Earned 100,000 credits (496,000)GFN Emerald: Earned 50,000,000 credits (64,937,531)PSA Emerald: Earned 50,000,000 credits (87,901,787)
Message 78255 - Posted: 22 Jul 2014 | 19:58:00 UTC - in response to Message 78248.

Grabbed another one today! :)
147348089501325541 (-1 -360 p)


:thumbup: Grats!
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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 78532 - Posted: 4 Aug 2014 | 21:28:28 UTC

Today zzuupp found the sixth near-Wieferich of 2014, p = 149648763777446677.

The last four near-Wieferichs have all been congruent to 5 (or -3) modulo 8.

/JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 78996 - Posted: 24 Aug 2014 | 13:29:55 UTC

User brinktastee found 152898977773687601 (+1 +241 p). This time a "+1" prime (p == 601 == 1 (mod 8)).

The value |A|/p = 241/152898977773687601 = 1.5762e-15 measures the "nearness".

/JeppeSN

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Discovered 2 mega primesFound 2 primes in the 2018 Tour de PrimesFound 2 primes in the 2019 Tour de PrimesFound 12 primes in the 2020 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,244,909)Cullen LLR Turquoise: Earned 5,000,000 credits (8,336,430)ESP LLR Turquoise: Earned 5,000,000 credits (5,174,327)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,028,260)PPS LLR Emerald: Earned 50,000,000 credits (59,236,744)PSP LLR Turquoise: Earned 5,000,000 credits (5,151,448)SoB LLR Turquoise: Earned 5,000,000 credits (5,014,268)SR5 LLR Jade: Earned 10,000,000 credits (14,871,275)SGS LLR Turquoise: Earned 5,000,000 credits (7,860,522)TRP LLR Jade: Earned 10,000,000 credits (11,130,742)Woodall LLR Turquoise: Earned 5,000,000 credits (5,419,909)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (101,538,236)Cullen/Woodall Sieve (suspended) Double Bronze: Earned 100,000,000 credits (127,922,665)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (30,984,158)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,840,173,136)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,134,964)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (7,013,696)AP 26/27 Double Silver: Earned 200,000,000 credits (276,723,135)WW Turquoise: Earned 5,000,000 credits (6,856,000)GFN Double Silver: Earned 200,000,000 credits (293,113,761)PSA Double Amethyst: Earned 1,000,000,000 credits (1,370,700,486)
Message 79051 - Posted: 26 Aug 2014 | 14:47:24 UTC - in response to Message 78996.

User brinktastee found 152898977773687601 (+1 +241 p). This time a "+1" prime (p == 601 == 1 (mod 8)).

The value |A|/p = 241/152898977773687601 = 1.5762e-15 measures the "nearness".

/JeppeSN


Congrats B!!!

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79065 - Posted: 26 Aug 2014 | 23:33:29 UTC
Last modified: 26 Aug 2014 | 23:34:22 UTC

Now 1998golfer found his first near-Wieferich, 155993139654086299 (-1 +714 p). With p == 299 == 3 (mod 8), and 714/155993139654086299 = 4.6e-15.

Now eight near-Wieferichs in 2014 (which is less than eight months old). Since we have a challenge in September, we will probably find more.

When a near-Wieferich is defined as one where A is between -1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 near-Wieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 near-Wieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.

/JeppeSN

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Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,238,816)Cullen LLR Turquoise: Earned 5,000,000 credits (5,124,261)ESP LLR Turquoise: Earned 5,000,000 credits (8,479,525)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,656,837)PPS LLR Sapphire: Earned 20,000,000 credits (23,348,483)PSP LLR Sapphire: Earned 20,000,000 credits (37,386,303)SoB LLR Sapphire: Earned 20,000,000 credits (21,004,651)SR5 LLR Sapphire: Earned 20,000,000 credits (33,215,655)SGS LLR Turquoise: Earned 5,000,000 credits (5,000,408)TRP LLR Jade: Earned 10,000,000 credits (12,199,250)Woodall LLR Turquoise: Earned 5,000,000 credits (6,931,665)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,012,059)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (27,921,016)PPS Sieve Double Gold: Earned 500,000,000 credits (542,336,593)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (7,990,608)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,217,057)AP 26/27 Turquoise: Earned 5,000,000 credits (5,773,404)WW Gold: Earned 500,000 credits (624,000)GFN Sapphire: Earned 20,000,000 credits (28,086,853)PSA Double Silver: Earned 200,000,000 credits (420,586,383)
Message 79072 - Posted: 27 Aug 2014 | 2:47:27 UTC - in response to Message 79065.

Now 1998golfer found his first near-Wieferich, 155993139654086299 (-1 +714 p). With p == 299 == 3 (mod 8), and 714/155993139654086299 = 4.6e-15.

Now eight near-Wieferichs in 2014 (which is less than eight months old). Since we have a challenge in September, we will probably find more.

When a near-Wieferich is defined as one where A is between -1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 near-Wieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 near-Wieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.

/JeppeSN

Oooh cool. Didn't even notice. I didn't get an email for this, nor for my near-WSS a while back.
Thanks for posting!
____________

275*2^3585539+1 is prime!!! (1079358 digits)

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Message 79076 - Posted: 27 Aug 2014 | 8:48:28 UTC - in response to Message 79065.

When a near-Wieferich is defined as one where A is between -1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 near-Wieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 near-Wieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.

How are we doing on WSS using similar metric?
____________
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Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79085 - Posted: 27 Aug 2014 | 21:38:31 UTC - in response to Message 79076.
Last modified: 27 Aug 2014 | 21:40:24 UTC

When a near-Wieferich is defined as one where A is between -1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 near-Wieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 near-Wieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.

How are we doing on WSS using similar metric?


That is more or less the same!

Again we calculate some value modulo p^2, again we know what it will be (0) mod p, so mod p^2 we have 0 + A*p. That A could be any integer between -p/2 and +p/2. When A is between -1000 and +1000, we call that "near". When A=0, that is a Wall-Sūn-Sūn.

So the probability of a near-Wall-Sūn-Sūn is 2000 times the probability of a real Wall-Sūn-Sūn.

PRPNet has found 218 near-WSS. We expect to find 2000 near-WSS for each WSS on average, in the long run.

(Our expectations could be wrong, of course, since there is no mathematical proof that the asymptotic behaviors is as conjectured.)

/JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79087 - Posted: 28 Aug 2014 | 10:22:59 UTC - in response to Message 79085.

When a near-Wieferich is defined as one where A is between -1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 near-Wieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 near-Wieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.

How are we doing on WSS using similar metric?


That is more or less the same!

Again we calculate some value modulo p^2, again we know what it will be (0) mod p, so mod p^2 we have 0 + A*p. That A could be any integer between -p/2 and +p/2. When A is between -1000 and +1000, we call that "near". When A=0, that is a Wall-Sūn-Sūn.

So the probability of a near-Wall-Sūn-Sūn is 2000 times the probability of a real Wall-Sūn-Sūn.

PRPNet has found 218 near-WSS. We expect to find 2000 near-WSS for each WSS on average, in the long run.

(Our expectations could be wrong, of course, since there is no mathematical proof that the asymptotic behaviors is as conjectured.)

/JeppeSN


Addition: This could be too naïve for Wall-Sūn-Sūn, though. For example Klaška's paper (free) says it is unlikely to find any Wall-Sūn-Sūns ending in 3 or 7 (i.e. with p == ±2 (mod 5)). So that gives only half the chance, namely primes ending in 1 or 9 (so p == ±1 (mod 5)). /JeppeSN

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Message 79090 - Posted: 28 Aug 2014 | 11:24:03 UTC - in response to Message 79087.

Addition: This could be too naïve for Wall-Sūn-Sūn, though. For example Klaška's paper (free) says it is unlikely to find any Wall-Sūn-Sūns ending in 3 or 7 (i.e. with p == ±2 (mod 5)). So that gives only half the chance, namely primes ending in 1 or 9 (so p == ±1 (mod 5)). /JeppeSN

Thanks for your thoughts and reference.

Anyone searching for a Fibonacci-Wieferich prime using a computer is facing
an immediate problem of completing the search of the interval [2 x 10^14,10^15]. By
(9), theoretically, there should be about 0.02 Fibonacci-Wieferich primes within
this interval ending with 1 or 9. In the following interval [10^15,10^16] then, there
should be about 0.03 primes. Even though the odds are not much favourable, there
is still hope that a Fibonacci-Wieferich prime will be discovered.

Well, I don't know how much this is encouraging but I'll give it a try again on my GTX580.

btw, it reminds me there is (semi)active non-BOINC Czech project on this subject.
http://www.elmath.org/.
Their CPU client wasn't optimized and due to lack of response from project stuff we have decided (Czech BOINC community] not to promote it.
Perhaps they have some theoretical papers on this subject as well.
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Message 79091 - Posted: 28 Aug 2014 | 14:04:58 UTC - in response to Message 79090.
Last modified: 28 Aug 2014 | 14:05:51 UTC

Multiply the 0.02 or 0.03 from that quote by 2000, and you get the number of near-WSS ending in 1 or 9 we expect to find in the same intervals, I guess. /JeppeSN

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Message 79093 - Posted: 28 Aug 2014 | 14:39:55 UTC

Fear not. There is a WSS challenge straight after the Wieferich Challenge.

Anyway, to get this thread back on track below is the full email reply to my query from François Dorais:

Dear Roger,

I just realized that you are not Zeta-Flux and that just made me read your message in a different light. I don't know who Zeta-Flux is so I can neither confirm nor deny the claim. He appears to have used an older version of WPSE but it wasn't buggy so I don't know why he is missing some data.

Anyway, I had a look at Primegrid which I now understand is not what Zeta-Flux was running. This is a great project! I checked your data against mine and I can confirm that your finding agree with ours up to 6.7e15.

I was a little puzzled by this remark:

Although the search for Wieferich primes reached an upper bound of 6.7e15, PrimeGrid's search will begin at 3e15. The reason for this is that Dorais and Klyve redefined what a "near" Wieferich prime was. Therefore, they did not search for "classical" "near" Wieferich primes. We do not expect to find any Wieferich primes between 3e15 and 6.7e15, but we do expect some "near" Wieferich primes. [EDIT - It appears that Dorais' and Klyve's definition did catch some "classical" "near" Wieferich primes but not all. We're searching for |A| < = 1000] <http://www.primegrid.com/forum_thread.php?id=3008&nowrap=true#45945>

I wish you had contacted us then to ask about this. It is true that we looked at different notions of near misses in our paper, but that doesn't mean we didn't search for "classical" near misses. In fact, since we were interested in the distribution of Fermat quotients, we had collected a very vast amount of data and we had a list of "classical" near misses for |A| <= 600000. The reason we "redefined" near misses is that the relative size version gives more accurate results for measuring distribution.

There is one important difference in that we used "full" Fermat quotients, i.e. A such that 2^{p-1} = 1 + pA (mod p^2), rather than "half" Fermat quotients, i.e. 2^{(p-1)/2} = (+/-)1 + pA (mod p^2). Fortunately, since ((+/-)1 + pA)^2 = 1 +/- 2pA (mod p^2), it's straightforward to recover the list of small "half" Fermat quotients from the list of small "full" Fermat quotients. I did that to check my list with yours and I'm happy to report that our lists agree on the overlap.

By the way, it would be nice if your data was available in plain CSV format. It was a bit of a pain to manually check against your PDF file. I also couldn't find a link to your code. Is it available?

Best wishes,

François

You'll be pleased to know we've fixed up the Primegrid reference François is mentioning.

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Message 79094 - Posted: 28 Aug 2014 | 15:31:03 UTC - in response to Message 79093.

Roger,

Note that the Wikipedia section was recently updated to describe the relation between the "A" in our project, related to 2^{(p-1)/2}, and the "A" belonging to the square of that, 2^{p-1}. This relation is trivial, one doubling modulo p.

When the first "A" is close to zero numerically, so is its "double" mod p. However, when the non-classical "A" is close to zero in this way, its "half" may be very far from zero, depending on whether the non-classical "A" was odd or even.

/JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79095 - Posted: 28 Aug 2014 | 15:43:33 UTC - in response to Message 79093.

Regarding the absolute size |A| and the relative |A/p|, note that I have started to calculate |A|/p for finds, in this thread. Because "we" (PRPNet's WFS project) stick to |A| <= 1000 no matter how big p gets, we will get very few near-Wieferichs.

A relative size requirement like |A|/p < 10^{-14} should in theory keep producing a "constant" flux of near-Wieferichs (by that altered definition).

/JeppeSN

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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 79108 - Posted: 29 Aug 2014 | 12:42:06 UTC - in response to Message 79095.
Last modified: 29 Aug 2014 | 12:47:20 UTC

Regarding the absolute size |A| and the relative |A/p|, note that I have started to calculate |A|/p for finds, in this thread. Because "we" (PRPNet's WFS project) stick to |A| <= 1000 no matter how big p gets, we will get very few near-Wieferichs.

A relative size requirement like |A|/p < 10^{-14} should in theory keep producing a "constant" flux of near-Wieferichs (by that altered definition).

/JeppeSN

Using the definition of near as A/p < 10^{-14}
With the lead currently at 1.587e17, |A| would have to be < 1587 to be "near".
That sounds reasonable.

92.000e17 is the upperbound that the current software can search to.
At that level |A| would have to be < 92000 to be "near".
That sounds reasonable as well.

Near finds are getting far apart, but we don't want to devalue them.
If rogue can modify wwww to support this it would have my support.

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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 79131 - Posted: 30 Aug 2014 | 13:13:16 UTC
Last modified: 30 Aug 2014 | 13:47:57 UTC

A crude way to implement this change is to just to add the following lines into the wwww/WWWW.cpp function:

void WWWW::Validate(void) ... if (ii_SearchType == 1 && !memcmp(line, "wieferich_special=", 18)) ii_SpecialThreshold = atoi(line+18); ...

Compile the app then just add the following to the wwww.ini file that's read at run time:
wieferich_special=1559 // current completed 155,912,600,000,000,000

There are other ways to do this but this one is configurable by the PRPNet user. Whether the Wieferich PRPNet Server would accept a special value above 1000 is another question. That value is hard coded.

Even without this change you can have fun testing the effect of changing the limit "-s switch" for determining special instances:
>wwwwcl -p0e4 -P1e4 -TWieferich -s100 -v

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79132 - Posted: 30 Aug 2014 | 13:33:37 UTC - in response to Message 79108.

Regarding the absolute size |A| and the relative |A/p|, note that I have started to calculate |A|/p for finds, in this thread. Because "we" (PRPNet's WFS project) stick to |A| <= 1000 no matter how big p gets, we will get very few near-Wieferichs.

A relative size requirement like |A|/p < 10^{-14} should in theory keep producing a "constant" flux of near-Wieferichs (by that altered definition).

/JeppeSN

Using the definition of near as A/p < 10^{-14}
With the lead currently at 1.587e17, |A| would have to be < 1587 to be "near".
That sounds reasonable.

92.000e17 is the upperbound that the current software can search to.
At that level |A| would have to be < 92000 to be "near".
That sounds reasonable as well.

Near finds are getting far apart, but we don't want to devalue them.
If rogue can modify wwww to support this it would have my support.


Dorais and Klyve in their Table 4 (top of page 11) actually list all with |A|/p < 10^{-13}, so that is ten times as many. (As I said earlier, their "A" corresponds to 2^{p-1}, not 2^{(p-1)/2}.)

/JeppeSN

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Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 79133 - Posted: 30 Aug 2014 | 14:22:58 UTC - in response to Message 79132.

Dorais and Klyve in their Table 4 (top of page 11) actually list all with |A|/p < 10^{-13}, so that is ten times as many. (As I said earlier, their "A" corresponds to 2^{p-1}, not 2^{(p-1)/2}.)

/JeppeSN

Dorais and Klyve were trying to create statistics on Near Finds for analysis, we're not doing that so |A|/p < 10^{-14} is enough.

Note that the Wikipedia section was recently updated to describe the relation between the "A" in our project, related to 2^{(p-1)/2}, and the "A" belonging to the square of that, 2^{p-1}. This relation is trivial, one doubling modulo p.

When the first "A" is close to zero numerically, so is its "double" mod p. However, when the non-classical "A" is close to zero in this way, its "half" may be very far from zero, depending on whether the non-classical "A" was odd or even.

So when we have a Near Find using "half" Fermat quotients it is also a Near Find using "full" Fermat quotients, such as Dorais and Klyve used, however the reverse is not always true. If that's correct then I am thinking that it would be better to search using "full" Fermat quotients so you don't miss anything interesting.

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79134 - Posted: 30 Aug 2014 | 14:45:43 UTC - in response to Message 79133.



[...]

So when we have a Near Find using "half" Fermat quotients it is also a Near Find using "full" Fermat quotients, such as Dorais and Klyve used, however the reverse is not always true. If that's correct then I am thinking that it would be better to search using "full" Fermat quotients so you don't miss anything interesting.


Absolutely correct, as far as I know. /JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79139 - Posted: 30 Aug 2014 | 19:19:49 UTC

Many finds right now, just before the challenge starts this Monday.

brinktastee found 159941928418171813 (-1 -775 p). With p == 813 == 5 (mod 8), and |A|/p = 775/159941928418171813 = 4.8e-15.

/JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79143 - Posted: 31 Aug 2014 | 6:38:18 UTC

Scott_Brown found 160388140707579713 (+1 +850 p); with p == 713 == 1 (mod 8), and 850/160388140707579713 = 5.3e-15.

When the around the wwwworld challenge runs (entire September 2014), I will not report individual near-Wieferichs in this thread.

/JeppeSN

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79856 - Posted: 1 Oct 2014 | 11:34:05 UTC - in response to Message 79143.

Scott_Brown found 160388140707579713 (+1 +850 p); with p == 713 == 1 (mod 8), and 850/160388140707579713 = 5.3e-15.

When the around the wwwworld challenge runs (entire September 2014), I will not report individual near-Wieferichs in this thread.

/JeppeSN


That challenge found 31 near-Wieferichs, the smallest being 170164210886417897 and the largest 317133503989986679.

It found one false positive, 214714110964439699 (-1 +12113703224047600 p), erroneously given as 214714110964439699 (+16384 -29001 p).

/JeppeSN

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Discovered 2 mega primesFound 1 prime in the 2019 Tour de Primes321 LLR Jade: Earned 10,000,000 credits (10,334,077)Cullen LLR Turquoise: Earned 5,000,000 credits (5,010,955)ESP LLR Turquoise: Earned 5,000,000 credits (7,439,418)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,501,906)PPS LLR Sapphire: Earned 20,000,000 credits (26,697,006)PSP LLR Turquoise: Earned 5,000,000 credits (6,184,417)SoB LLR Jade: Earned 10,000,000 credits (12,120,365)SR5 LLR Turquoise: Earned 5,000,000 credits (9,234,440)SGS LLR Turquoise: Earned 5,000,000 credits (5,201,403)TRP LLR Turquoise: Earned 5,000,000 credits (5,628,223)Woodall LLR Turquoise: Earned 5,000,000 credits (5,061,985)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,027,534)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (17,370,919)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,014,372)PPS Sieve Double Bronze: Earned 100,000,000 credits (129,430,775)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,083,315)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,629,248)AP 26/27 Emerald: Earned 50,000,000 credits (56,876,924)GFN Double Silver: Earned 200,000,000 credits (286,079,854)PSA Double Silver: Earned 200,000,000 credits (200,556,062)
Message 79881 - Posted: 1 Oct 2014 | 17:42:22 UTC - in response to Message 79139.

Many finds right now, just before the challenge starts this Monday.

brinktastee found 159941928418171813 (-1 -775 p). With p == 813 == 5 (mod 8), and |A|/p = 775/159941928418171813 = 4.8e-15.

/JeppeSN

Did this near-find get found during the challenge?
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Message 79883 - Posted: 1 Oct 2014 | 18:00:51 UTC - in response to Message 79881.

Many finds right now, just before the challenge starts this Monday.

brinktastee found 159941928418171813 (-1 -775 p). With p == 813 == 5 (mod 8), and |A|/p = 775/159941928418171813 = 4.8e-15.

/JeppeSN

Did this near-find get found during the challenge?

sorry, no! if you check the whole findlist you will find a reporting date "Saturday 30th of August 2014 06:00:11 PM" and this is not in September ;)
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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 79885 - Posted: 1 Oct 2014 | 18:59:05 UTC - in response to Message 79883.

Many finds right now, just before the challenge starts this Monday.

brinktastee found 159941928418171813 (-1 -775 p). With p == 813 == 5 (mod 8), and |A|/p = 775/159941928418171813 = 4.8e-15.

/JeppeSN

Did this near-find get found during the challenge?

sorry, no! if you check the whole findlist you will find a reporting date "Saturday 30th of August 2014 06:00:11 PM" and this is not in September ;)


Also, the post (by me) being quoted is from August, and I am not able to predict which finds will be done in the future, and by whom ;-) No posts to this thread were done in September (UTC).

/JeppeSN

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Credit: 3,622,648
RAC: 0
321 LLR Silver: Earned 100,000 credits (102,041)Cullen LLR Bronze: Earned 10,000 credits (32,959)ESP LLR Bronze: Earned 10,000 credits (83,243)PPS LLR Silver: Earned 100,000 credits (223,033)PSP LLR Silver: Earned 100,000 credits (131,571)SR5 LLR Bronze: Earned 10,000 credits (49,026)SGS LLR Bronze: Earned 10,000 credits (99,613)TRP LLR Silver: Earned 100,000 credits (261,144)Woodall LLR Silver: Earned 100,000 credits (164,341)321 Sieve (suspended) Bronze: Earned 10,000 credits (10,359)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (40,093)PPS Sieve Gold: Earned 500,000 credits (562,985)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (44,403)TRP Sieve (suspended) Silver: Earned 100,000 credits (102,453)AP 26/27 Bronze: Earned 10,000 credits (11,505)GFN Silver: Earned 100,000 credits (165,611)PSA Amethyst: Earned 1,000,000 credits (1,537,892)
Message 80297 - Posted: 14 Oct 2014 | 18:00:39 UTC

user team client value ▾ date reported MiHost AMD_Users Farscape2 82687771042557349 (-1 -10 p) Tuesday 15th of January 2013 04:49:41 PM JAMC My_Way 2 5131427559624857 (+1 -18 p) Tuesday 03rd of January 2012 10:51:51 PM Tarmo_Ilves Aggie_The_Pew server3 3723113065138349 (-1 +18 p) Saturday 31st of December 2011 04:31:52 PM [DPC]Pyrus Dutch_Power_Cows genghis 4150209531584437 (-1 -24 p) Monday 02nd of January 2012 12:21:06 AM brinktastee Aggie_The_Pew ASUS_I7_950 145172216558999221 (-1 +26 p) Monday 14th of July 2014 02:19:30 PM


all findings are pretty old still
____________
wbr, Me. Dead J. Dona

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Joined: 5 Apr 14
Posts: 1319
ID: 306875
Credit: 19,144,173
RAC: 37,458
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 80307 - Posted: 15 Oct 2014 | 12:35:12 UTC - in response to Message 80297.

Death[Kiev], it is easier for the absolute value of |A| to be small when p is small. /JeppeSN

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Joined: 5 Apr 14
Posts: 1319
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Credit: 19,144,173
RAC: 37,458
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 80831 - Posted: 18 Nov 2014 | 8:32:07 UTC

User composite found 325347156897384571 (-1 +361 p). His second near-Wieferich, and the greatest one ever found. It is 571 == 3 (mod 8). |A|/p = 361/325347156897384571 = 1.1e-15. /JeppeSN

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Joined: 5 Apr 14
Posts: 1319
ID: 306875
Credit: 19,144,173
RAC: 37,458
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 84733 - Posted: 10 Apr 2015 | 5:43:43 UTC

If you use PARI/GP, you can check our Wieferich finds very easily with this function:

checkWieferich(p) = { if(!isprime(p)||p==2,return("no, p is not an odd prime")); plusOrMinus = kronecker(2,p); result = centerlift(Mod(2,p^2)^((p-1)/2)); result = (result-plusOrMinus)/p; Strprintf("%d (%+d %+d p)", p, plusOrMinus, result) }


I posted similar code in the September 2014 challenge thread.

If you use this to check huge numbers, consider using ispseudoprime method instead of isprime, in the top of the function "body".

/JeppeSN

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Joined: 27 Nov 11
Posts: 1137
ID: 120786
Credit: 267,278,751
RAC: 8,580
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,037,982)Cullen LLR Ruby: Earned 2,000,000 credits (2,015,907)ESP LLR Ruby: Earned 2,000,000 credits (2,232,391)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,962,062)PSP LLR Ruby: Earned 2,000,000 credits (2,539,644)SoB LLR Ruby: Earned 2,000,000 credits (2,122,524)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (3,892,674)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,037,732)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,049,697)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,651,644)GFN Emerald: Earned 50,000,000 credits (57,918,585)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 88800 - Posted: 7 Oct 2015 | 14:07:06 UTC

Looks like I just found 494997492935398501 (-1 +470 p). With p == 501 == 5 (mod 8), and |A|/p = 470/494997492935398501 = 9.495e-16.
This is my 8th near find and best |A|/p so far!
A good finish to Wieferich season for me.

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Joined: 5 Apr 14
Posts: 1319
ID: 306875
Credit: 19,144,173
RAC: 37,458
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (590,417)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,725,441)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (105,212)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Silver: Earned 100,000 credits (160,076)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 88811 - Posted: 7 Oct 2015 | 20:46:12 UTC - in response to Message 88800.

Congratulations. /JeppeSN

Message boards : Project Staging Area : Wieferich - it has been a while

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