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Message boards : Generalized Fermat Prime Search : 919444^1048576+1 is prime!

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Profile Michael GoetzProject donor
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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 Primes321 LLR Ruby: Earned 2,000,000 credits (2,046,746)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (2,001,789)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,004,898)PPS LLR Ruby: Earned 2,000,000 credits (2,082,200)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (24,608,301)SR5 LLR Turquoise: Earned 5,000,000 credits (7,369,317)SGS LLR Ruby: Earned 2,000,000 credits (2,010,466)TRP LLR Ruby: Earned 2,000,000 credits (2,433,520)Woodall LLR Ruby: Earned 2,000,000 credits (2,012,392)321 Sieve (suspended) Silver: Earned 100,000 credits (200,576)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (3,622,411)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)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 Turquoise: Earned 5,000,000 credits (7,086,053)GFN Emerald: Earned 50,000,000 credits (52,696,917)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 109815 - Posted: 2 Sep 2017 | 15:15:55 UTC

The first known GFN n=20 prime has been found!!!

On the 29th of August, 2017, at 14:15:23 UTC, one of Van Zimmerman's computers discovered the first known n=20 GFN prime. The discovery was made on a GTX 1060 3 GB GPU.

Primality checks were performed internally using both the -p version of Genefer on GPUs and LLR on CPUs. We waited until the LLR tests completed today to announce the discovery.

The search for a GFN 20 was started shortly after we discovered the first known GFN 19, almost five years ago. Congratulations to Van Zimmerman on this long overdue discovery!

This prime is 6,253,210 digits in length, and is (of course) the largest known Generalized Fermat Prime, and the 12th largest known prime overall.

T5K entry is here: http://primes.utm.edu/primes/page.php?id=123875
____________
Please do not PM me with support questions. Ask on the forums instead. Thank you!

My lucky number is 75898524288+1

Profile Rick Reynolds
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Discovered 1 mega primeFound 2 primes in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,148,880)Cullen LLR Ruby: Earned 2,000,000 credits (2,773,730)ESP LLR Ruby: Earned 2,000,000 credits (2,084,793)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,686,707)PPS LLR Jade: Earned 10,000,000 credits (11,171,386)PSP LLR Amethyst: Earned 1,000,000 credits (1,932,735)SoB LLR Ruby: Earned 2,000,000 credits (2,798,257)SR5 LLR Jade: Earned 10,000,000 credits (11,169,992)SGS LLR Turquoise: Earned 5,000,000 credits (6,112,229)TRP LLR Turquoise: Earned 5,000,000 credits (5,110,887)Woodall LLR Ruby: Earned 2,000,000 credits (3,612,313)321 Sieve (suspended) Bronze: Earned 10,000 credits (54,591)Cullen/Woodall Sieve (suspended) Double Bronze: Earned 100,000,000 credits (127,922,665)Generalized Cullen/Woodall Sieve Jade: Earned 10,000,000 credits (12,229,552)PPS Sieve Double Amethyst: Earned 1,000,000,000 credits (1,655,954,320)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 Bronze: Earned 100,000,000 credits (105,817,439)GFN Double Bronze: Earned 100,000,000 credits (110,780,411)PSA Double Amethyst: Earned 1,000,000,000 credits (1,370,700,486)
Message 109822 - Posted: 2 Sep 2017 | 15:42:13 UTC

Congrats on this great find V-man!

Cheers
____________
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Anthony Ayiomamitis
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321 LLR Ruby: Earned 2,000,000 credits (2,035,398)Cullen LLR Ruby: Earned 2,000,000 credits (2,047,548)ESP LLR Ruby: Earned 2,000,000 credits (2,033,639)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,014,465)PPS LLR Ruby: Earned 2,000,000 credits (2,554,144)PSP LLR Ruby: Earned 2,000,000 credits (2,107,810)SoB LLR Ruby: Earned 2,000,000 credits (2,017,375)SR5 LLR Ruby: Earned 2,000,000 credits (2,023,400)SGS LLR Ruby: Earned 2,000,000 credits (2,027,208)TRP LLR Ruby: Earned 2,000,000 credits (2,045,113)Woodall LLR Ruby: Earned 2,000,000 credits (2,097,219)Generalized Cullen/Woodall Sieve Emerald: Earned 50,000,000 credits (78,701,608)PPS Sieve Double Silver: Earned 200,000,000 credits (240,102,846)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (14,516,062)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,329,228)AP 26/27 Sapphire: Earned 20,000,000 credits (20,275,645)GFN Sapphire: Earned 20,000,000 credits (21,981,135)PSA Double Bronze: Earned 100,000,000 credits (116,531,700)
Message 109828 - Posted: 2 Sep 2017 | 16:32:25 UTC - in response to Message 109822.

This is awesome news. Many congrats Zimmer!

Van ZimmermanProject donor
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Discovered the World's First GFN-20 prime!!!Discovered 2 mega primesFound 1 prime in the 2018 Tour de Primes321 LLR Sapphire: Earned 20,000,000 credits (20,089,185)Cullen LLR Sapphire: Earned 20,000,000 credits (21,197,588)ESP LLR Sapphire: Earned 20,000,000 credits (20,089,407)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (20,037,992)PPS LLR Sapphire: Earned 20,000,000 credits (21,122,874)PSP LLR Sapphire: Earned 20,000,000 credits (20,117,197)SoB LLR Sapphire: Earned 20,000,000 credits (21,208,789)SR5 LLR Sapphire: Earned 20,000,000 credits (20,278,667)SGS LLR Sapphire: Earned 20,000,000 credits (20,055,153)TRP LLR Sapphire: Earned 20,000,000 credits (20,619,871)Woodall LLR Sapphire: Earned 20,000,000 credits (20,376,227)Generalized Cullen/Woodall Sieve Sapphire: Earned 20,000,000 credits (20,371,066)PPS Sieve Double Amethyst: Earned 1,000,000,000 credits (1,051,222,753)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,189,695)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,102,079)AP 26/27 Emerald: Earned 50,000,000 credits (60,248,786)GFN Double Ruby: Earned 2,000,000,000 credits (3,809,402,618)PSA Double Bronze: Earned 100,000,000 credits (194,620,077)
Message 109832 - Posted: 2 Sep 2017 | 16:43:23 UTC - in response to Message 109828.

Many thanks all!
____________
I have 919444^1048576+1 reasons to be crunching more GFN.

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Discovered 1 AP26321 LLR Gold: Earned 500,000 credits (512,718)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (272,624)PPS LLR Ruby: Earned 2,000,000 credits (3,400,474)SoB LLR Gold: Earned 500,000 credits (505,877)SR5 LLR Gold: Earned 500,000 credits (656,233)SGS LLR Amethyst: Earned 1,000,000 credits (1,645,196)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,567,960)PPS Sieve Double Silver: Earned 200,000,000 credits (358,451,914)TRP Sieve (suspended) Silver: Earned 100,000 credits (304,200)AP 26/27 Jade: Earned 10,000,000 credits (14,344,564)GFN Sapphire: Earned 20,000,000 credits (26,555,670)
Message 109833 - Posted: 2 Sep 2017 | 16:47:45 UTC

Wow, what a find!!!! Congratulations Zimmer! :-)

Profile Rafael
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321 LLR Ruby: Earned 2,000,000 credits (4,564,140)Cullen LLR Ruby: Earned 2,000,000 credits (4,563,655)ESP LLR Ruby: Earned 2,000,000 credits (4,527,638)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (4,524,108)PPS LLR Ruby: Earned 2,000,000 credits (4,378,563)PSP LLR Ruby: Earned 2,000,000 credits (4,545,606)SoB LLR Ruby: Earned 2,000,000 credits (4,057,135)SR5 LLR Ruby: Earned 2,000,000 credits (4,429,958)SGS LLR Ruby: Earned 2,000,000 credits (4,285,716)TRP LLR Ruby: Earned 2,000,000 credits (4,608,089)Woodall LLR Ruby: Earned 2,000,000 credits (4,652,346)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (4,246,236)PPS Sieve Turquoise: Earned 5,000,000 credits (5,214,937)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,053)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,030,160)AP 26/27 Ruby: Earned 2,000,000 credits (3,157,583)GFN Sapphire: Earned 20,000,000 credits (22,870,682)PSA Double Bronze: Earned 100,000,000 credits (133,881,279)
Message 109837 - Posted: 2 Sep 2017 | 17:42:01 UTC

PogChamp

And to think I was crunching n=20 just a couple of days ago, stopping to do Manual Sieve...

Profile AzmodesProject donor
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Discovered 1 AP26Found 2 primes in the 2018 Tour de Primes321 LLR Silver: Earned 100,000 credits (396,886)Cullen LLR Bronze: Earned 10,000 credits (12,687)ESP LLR Bronze: Earned 10,000 credits (14,780)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (25,006)PPS LLR Amethyst: Earned 1,000,000 credits (1,007,852)PSP LLR Bronze: Earned 10,000 credits (10,031)SoB LLR Silver: Earned 100,000 credits (141,395)SR5 LLR Gold: Earned 500,000 credits (542,747)SGS LLR Gold: Earned 500,000 credits (516,800)TRP LLR Bronze: Earned 10,000 credits (11,255)Woodall LLR Gold: Earned 500,000 credits (505,988)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (6,138,495)PPS Sieve Double Silver: Earned 200,000,000 credits (235,936,290)TRP Sieve (suspended) Bronze: Earned 10,000 credits (39,046)AP 26/27 Sapphire: Earned 20,000,000 credits (27,783,496)GFN Sapphire: Earned 20,000,000 credits (40,129,873)PSA Double Silver: Earned 200,000,000 credits (263,425,955)
Message 109839 - Posted: 2 Sep 2017 | 17:48:42 UTC
Last modified: 2 Sep 2017 | 17:49:33 UTC

Awesome, congrats!

rvoskoboynikov
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Discovered 1 mega primeFound 1 prime in the 2018 Tour de Primes321 LLR Silver: Earned 100,000 credits (175,356)Cullen LLR Silver: Earned 100,000 credits (174,572)ESP LLR Silver: Earned 100,000 credits (121,328)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (341,146)PPS LLR Turquoise: Earned 5,000,000 credits (9,359,272)PSP LLR Silver: Earned 100,000 credits (141,489)SoB LLR Ruby: Earned 2,000,000 credits (2,143,146)SR5 LLR Silver: Earned 100,000 credits (162,872)SGS LLR Ruby: Earned 2,000,000 credits (2,021,102)TRP LLR Silver: Earned 100,000 credits (366,858)Woodall LLR Silver: Earned 100,000 credits (217,132)Generalized Cullen/Woodall Sieve Gold: Earned 500,000 credits (656,417)PPS Sieve Jade: Earned 10,000,000 credits (10,099,516)AP 26/27 Jade: Earned 10,000,000 credits (10,895,885)GFN Sapphire: Earned 20,000,000 credits (28,299,466)PSA Turquoise: Earned 5,000,000 credits (5,023,220)
Message 109842 - Posted: 2 Sep 2017 | 18:51:42 UTC

Time to place bets on when the first GFN-21 prime is found.

Van ZimmermanProject donor
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Discovered the World's First GFN-20 prime!!!Discovered 2 mega primesFound 1 prime in the 2018 Tour de Primes321 LLR Sapphire: Earned 20,000,000 credits (20,089,185)Cullen LLR Sapphire: Earned 20,000,000 credits (21,197,588)ESP LLR Sapphire: Earned 20,000,000 credits (20,089,407)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (20,037,992)PPS LLR Sapphire: Earned 20,000,000 credits (21,122,874)PSP LLR Sapphire: Earned 20,000,000 credits (20,117,197)SoB LLR Sapphire: Earned 20,000,000 credits (21,208,789)SR5 LLR Sapphire: Earned 20,000,000 credits (20,278,667)SGS LLR Sapphire: Earned 20,000,000 credits (20,055,153)TRP LLR Sapphire: Earned 20,000,000 credits (20,619,871)Woodall LLR Sapphire: Earned 20,000,000 credits (20,376,227)Generalized Cullen/Woodall Sieve Sapphire: Earned 20,000,000 credits (20,371,066)PPS Sieve Double Amethyst: Earned 1,000,000,000 credits (1,051,222,753)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,189,695)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,102,079)AP 26/27 Emerald: Earned 50,000,000 credits (60,248,786)GFN Double Ruby: Earned 2,000,000,000 credits (3,809,402,618)PSA Double Bronze: Earned 100,000,000 credits (194,620,077)
Message 109843 - Posted: 2 Sep 2017 | 19:14:46 UTC - in response to Message 109842.

Time to place bets on when the first GFN-21 prime is found.


Indeed, and I believe the pool for n=20 needs to be worked out.

Iain BethuneProject donor
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321 LLR Gold: Earned 500,000 credits (597,175)Cullen LLR Amethyst: Earned 1,000,000 credits (1,355,381)ESP LLR Turquoise: Earned 5,000,000 credits (5,048,594)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,564,412)PPS LLR Amethyst: Earned 1,000,000 credits (1,025,115)PSP LLR Sapphire: Earned 20,000,000 credits (28,367,849)SoB LLR Jade: Earned 10,000,000 credits (13,662,809)SR5 LLR Turquoise: Earned 5,000,000 credits (5,189,992)SGS LLR Amethyst: Earned 1,000,000 credits (1,244,067)TRP LLR Turquoise: Earned 5,000,000 credits (5,169,405)Woodall LLR Amethyst: Earned 1,000,000 credits (1,070,956)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,003)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (200,371)Generalized Cullen/Woodall Sieve Jade: Earned 10,000,000 credits (11,645,025)PPS Sieve Turquoise: Earned 5,000,000 credits (7,536,532)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,017,144)TRP Sieve (suspended) Gold: Earned 500,000 credits (554,946)AP 26/27 Ruby: Earned 2,000,000 credits (3,577,848)GFN Emerald: Earned 50,000,000 credits (97,047,976)PSA Ruby: Earned 2,000,000 credits (4,606,694)
Message 109846 - Posted: 2 Sep 2017 | 19:34:19 UTC

Congrats to Van on the find (and also to all the others who crunched the WUs leading up to this one)!

- Iain
____________
Twitter: IainBethune
Proud member of team "Aggie The Pew". Go Aggie!
3073428256125*2^1290000-1 is Prime!

JeppeSNProject donor
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321 LLR Bronze: Earned 10,000 credits (48,835)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Bronze: Earned 10,000 credits (13,226)PPS LLR Amethyst: Earned 1,000,000 credits (1,611,251)SoB LLR Silver: Earned 100,000 credits (132,293)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (14,746)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 109849 - Posted: 2 Sep 2017 | 19:51:31 UTC

That is really awesome. And I see Van Zimmerman has had the joy of announcing his own find in the News subforum now. Congratulations and thanks for your work. /JeppeSN

Yves Gallot
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GFN Double Silver: Earned 200,000,000 credits (230,128,050)
Message 109851 - Posted: 2 Sep 2017 | 21:04:15 UTC

Champagne!
Congratulations, a great reward after 2,000,000,000 GFN credits!

KeithProject donor
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Found 2 primes in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,438,872)Cullen LLR Turquoise: Earned 5,000,000 credits (5,009,911)ESP LLR Ruby: Earned 2,000,000 credits (2,279,697)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,003,159)PPS LLR Ruby: Earned 2,000,000 credits (2,661,511)PSP LLR Ruby: Earned 2,000,000 credits (2,436,657)SoB LLR Turquoise: Earned 5,000,000 credits (5,031,081)SR5 LLR Turquoise: Earned 5,000,000 credits (5,004,943)SGS LLR Ruby: Earned 2,000,000 credits (3,062,685)TRP LLR Turquoise: Earned 5,000,000 credits (5,003,400)Woodall LLR Ruby: Earned 2,000,000 credits (4,923,561)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,004,494)PPS Sieve Emerald: Earned 50,000,000 credits (66,664,896)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,002,980)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,010,755)AP 26/27 Emerald: Earned 50,000,000 credits (50,003,824)GFN Emerald: Earned 50,000,000 credits (50,644,843)
Message 109855 - Posted: 2 Sep 2017 | 21:33:04 UTC

Now we should all flip over to GFN-21 and see what happens.

Congrats to Van Zimmerman and the still unknown doublechecker!
And well done to everyone who crunched a GFN-20 unit to this point!
____________
My Primes
Badge Score: 4*2 + 5*7 + 6*5 + 9*3 = 100

JeppeSNProject donor
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321 LLR Bronze: Earned 10,000 credits (48,835)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Bronze: Earned 10,000 credits (13,226)PPS LLR Amethyst: Earned 1,000,000 credits (1,611,251)SoB LLR Silver: Earned 100,000 credits (132,293)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (14,746)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 109859 - Posted: 2 Sep 2017 | 22:16:45 UTC

I tried to make a list of previous finds of this significance.

919444^(2^20) + 1

919444^(2^20) + 1 2017-Sep-02 Sylvanus A. Zimmerman (PrimeGrid)
75898^(2^19) + 1
75898^(2^19) + 1 2011-Nov-19 Michael Goetz (PrimeGrid)
24518^(2^18) + 1
24518^(2^18) + 1 2008-Mar-12 Stephen Scott
62722^(2^17) + 1
62722^(2^17) + 1 2003-Feb-16 Michael Angel
48594^(2^16) + 1
48594^(2^16) + 1 2000-Jun-07 Stephen Scott
70906^(2^15) + 1
70906^(2^15) + 1 2001-May-08 Pavlos Saridis
67234^(2^14) + 1
67234^(2^14) + 1 1999-Jun-07 Yves Gallot
30406^(2^13) + 1
30406^(2^13) + 1 1999-Feb-11 Yves Gallot
1534^(2^12) + 1
1534^(2^12) + 1 1994-Aug Harvey Dubner
150^(2^11) + 1
150^(2^11) + 1 1986 Harvey Dubner
824^(2^10) + 1
824^(2^10) + 1 1986 Harvey Dubner


The links are my source, Caldwell's Prime Pages.

/JeppeSN

gazzyk1ns
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321 LLR Amethyst: Earned 1,000,000 credits (1,446,317)Cullen LLR Amethyst: Earned 1,000,000 credits (1,206,959)ESP LLR Ruby: Earned 2,000,000 credits (2,039,070)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,150,104)PPS LLR Amethyst: Earned 1,000,000 credits (1,298,005)PSP LLR Turquoise: Earned 5,000,000 credits (5,524,288)SoB LLR Jade: Earned 10,000,000 credits (19,643,178)SR5 LLR Ruby: Earned 2,000,000 credits (2,014,726)SGS LLR Amethyst: Earned 1,000,000 credits (1,085,939)TRP LLR Turquoise: Earned 5,000,000 credits (5,262,750)Woodall LLR Ruby: Earned 2,000,000 credits (2,035,102)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,190,376)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,651,496)PPS Sieve Double Bronze: Earned 100,000,000 credits (196,036,913)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,591,642)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,819,072)AP 26/27 Ruby: Earned 2,000,000 credits (2,150,876)GFN Sapphire: Earned 20,000,000 credits (22,745,052)PSA Sapphire: Earned 20,000,000 credits (38,445,145)
Message 109860 - Posted: 2 Sep 2017 | 22:17:55 UTC

Prime congRATulations Van Zimmerman!

Profile Michael GoetzProject donor
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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 Primes321 LLR Ruby: Earned 2,000,000 credits (2,046,746)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (2,001,789)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,004,898)PPS LLR Ruby: Earned 2,000,000 credits (2,082,200)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (24,608,301)SR5 LLR Turquoise: Earned 5,000,000 credits (7,369,317)SGS LLR Ruby: Earned 2,000,000 credits (2,010,466)TRP LLR Ruby: Earned 2,000,000 credits (2,433,520)Woodall LLR Ruby: Earned 2,000,000 credits (2,012,392)321 Sieve (suspended) Silver: Earned 100,000 credits (200,576)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (3,622,411)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)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 Turquoise: Earned 5,000,000 credits (7,086,053)GFN Emerald: Earned 50,000,000 credits (52,696,917)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 109988 - Posted: 5 Sep 2017 | 20:20:47 UTC

https://www.theregister.co.uk/2017/09/05/new_colossal_prime_number/
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Discovered 7 mega primesEliminated 2 conjecture "k"sDiscovered 2 AP26sDiscovered 1 twin prime2017 Tour de Primes highest prime count2017 Tour de Primes most Mountain Stage primes2018 Tour de Primes most Mountain Stage primesFound 4 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 4 primes in the 2018 Tour de Primes Mountain StageFound 1 mega prime in the 2018 Tour de Primes Mountain Stage321 LLR Emerald: Earned 50,000,000 credits (52,964,603)Cullen LLR Emerald: Earned 50,000,000 credits (58,024,172)ESP LLR Emerald: Earned 50,000,000 credits (53,384,998)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (69,711,787)PPS LLR Double Bronze: Earned 100,000,000 credits (100,356,760)PSP LLR Emerald: Earned 50,000,000 credits (51,603,689)SoB LLR Double Bronze: Earned 100,000,000 credits (157,714,081)SR5 LLR Emerald: Earned 50,000,000 credits (52,541,942)SGS LLR Emerald: Earned 50,000,000 credits (54,944,236)TRP LLR Double Bronze: Earned 100,000,000 credits (105,766,411)Woodall LLR Emerald: Earned 50,000,000 credits (58,943,805)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,031,883)Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (30,879,764)Generalized Cullen/Woodall Sieve Double Bronze: Earned 100,000,000 credits (100,428,955)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (3,008,139,439)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Bronze: Earned 100,000,000 credits (101,857,516)TRP Sieve (suspended) Emerald: Earned 50,000,000 credits (50,936,081)AP 26/27 Double Gold: Earned 500,000,000 credits (700,506,352)GFN Double Ruby: Earned 2,000,000,000 credits (2,458,874,200)PSA Double Ruby: Earned 2,000,000,000 credits (4,572,823,040)
Message 109996 - Posted: 5 Sep 2017 | 23:11:11 UTC - in response to Message 109855.

Now we should all flip over to GFN-21 and see what happens.


There's still GFN-21 manual sieving work available.
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Message 109997 - Posted: 5 Sep 2017 | 23:27:46 UTC - in response to Message 109996.

There's still GFN-21 manual sieving work available.

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Message 112778 - Posted: 30 Dec 2017 | 13:04:12 UTC

Now all b<919444 have been double checked on n=20, so we have proof that

919444^(2^20) + 1

is the smallest n=20 generalized Fermat prime. /JeppeSN

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Message 112803 - Posted: 31 Dec 2017 | 9:47:27 UTC - in response to Message 112778.

Now all b<919444 have been double checked on n=20, so we have proof that
919444^(2^20) + 1

is the smallest n=20 generalized Fermat prime. /JeppeSN

This achievement is a major milestone this year.

It can be compared to "The 24th Fermat number is composite" in 1999.
F24 = 65536^(2^20) + 1 and proofs used this form.
http://www.ams.org/journals/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.pdf

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321 LLR Bronze: Earned 10,000 credits (48,835)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Bronze: Earned 10,000 credits (13,226)PPS LLR Amethyst: Earned 1,000,000 credits (1,611,251)SoB LLR Silver: Earned 100,000 credits (132,293)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (14,746)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 112812 - Posted: 31 Dec 2017 | 16:01:01 UTC - in response to Message 112803.

Now all b<919444 have been double checked on n=20, so we have proof that
919444^(2^20) + 1

is the smallest n=20 generalized Fermat prime. /JeppeSN

This achievement is a major milestone this year.

It can be compared to "The 24th Fermat number is composite" in 1999.
F24 = 65536^(2^20) + 1 and proofs used this form.
http://www.ams.org/journals/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.pdf


Yeah! So in 1999, doing a single test of GF(20, 65'536) (=F(24)), finding a composite, was worth publishing a paper for. And by the end of 2017, we have tested and double checked all GF(20, b) with b ≤ 919'444 (and a bit more).

Merry New Year! /JeppeSN

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Discovered 2 mega primesFound 1 prime in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,090,406)Cullen LLR Gold: Earned 500,000 credits (776,297)ESP LLR Amethyst: Earned 1,000,000 credits (1,542,446)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,719,804)PPS LLR Turquoise: Earned 5,000,000 credits (7,842,700)PSP LLR Ruby: Earned 2,000,000 credits (3,777,949)SoB LLR Jade: Earned 10,000,000 credits (13,047,850)SR5 LLR Turquoise: Earned 5,000,000 credits (5,978,312)SGS LLR Ruby: Earned 2,000,000 credits (2,896,483)TRP LLR Turquoise: Earned 5,000,000 credits (6,582,501)Woodall LLR Amethyst: Earned 1,000,000 credits (1,693,614)321 Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,228,005)Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,571,178)Generalized Cullen/Woodall Sieve Sapphire: Earned 20,000,000 credits (35,863,600)PPS Sieve Double Silver: Earned 200,000,000 credits (200,517,814)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,165,888)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,071,454)AP 26/27 Ruby: Earned 2,000,000 credits (2,544,827)GFN Sapphire: Earned 20,000,000 credits (34,868,164)PSA Double Bronze: Earned 100,000,000 credits (102,762,384)
Message 112814 - Posted: 31 Dec 2017 | 16:18:12 UTC - in response to Message 112812.


Yeah! So in 1999, doing a single test of GF(20, 65'536) (=F(24)), finding a composite, was worth publishing a paper for. And by the end of 2017, we have tested and double checked all GF(20, b) with b ≤ 919'444 (and a bit more).

Merry New Year! /JeppeSN

So you noticed they also said there are likely no more prime F(N) either, certainly none that could be tested with silicon ROFL.

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Message 112841 - Posted: 1 Jan 2018 | 4:21:41 UTC - in response to Message 112814.


Yeah! So in 1999, doing a single test of GF(20, 65'536) (=F(24)), finding a composite, was worth publishing a paper for. And by the end of 2017, we have tested and double checked all GF(20, b) with b ≤ 919'444 (and a bit more).

Merry New Year! /JeppeSN

So you noticed they also said there are likely no more prime F(N) either, certainly none that could be tested with silicon ROFL.


Why the "ROFL"? Do you know any more prime F(N)? (F(N) = Fermat number = 2^2^n+1, as opposed to GFN b^2^n+1)

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Message 112846 - Posted: 1 Jan 2018 | 5:25:31 UTC - in response to Message 112841.
Last modified: 1 Jan 2018 | 5:53:25 UTC

Yes I know. There isn't likely to be any more F(N). But in 1999, in spite of Moore's Law, nobody was expecting multicore computers in your pocket and supercomputers on your desktop, which is what we have today.

EDIT it's a commentary on the silicon. The use case just wasn't there for pocket computers AKA smart phones. If you played with a pocket calculator on the bus 40 years ago people looked at you weirdly, now people think you're weird if you don't have a pocket computing device.

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Message 112851 - Posted: 1 Jan 2018 | 8:05:52 UTC - in response to Message 112846.

EDIT it's a commentary on the silicon. The use case just wasn't there for pocket computers AKA smart phones. If you played with a pocket calculator on the bus 40 years ago people looked at you weirdly, now people think you're weird if you don't have a pocket computing device.


Ok. Perhaps you need to understand the fuller context of the "certainly none that could be tested with silicon" comment.

From http://www.prothsearch.com/fermat.html , you can see that F24 needed to be tested, since it didn't (doesn't) have any known factors. The next few (25..32) have known factors and doesn't need to be tested. So the next one that needs to be tested is F33 = 2^2^33+1, a 2.5 billion digit number. Even with the modern multi-core-this and GPU-that, there is no realistic hope of testing that in less than a decade (I'm being generous -- centuries might be more accurate). And each subsequent Fermat number doubles in size (and therefore takes 4-5x as much time to test as the previous one).

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Message 112854 - Posted: 1 Jan 2018 | 11:34:14 UTC - in response to Message 112851.

Also see Wikipedia's article Pépin's test. /JeppeSN

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