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Message boards : News : GFN-1048576 Mega Prime!

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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 PrimesFound 1 prime in the 2019 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 (21,873,609)PPS LLR Sapphire: Earned 20,000,000 credits (21,918,476)PSP LLR Sapphire: Earned 20,000,000 credits (20,117,197)SoB LLR Sapphire: Earned 20,000,000 credits (26,779,370)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 (20,394,541)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (28,148,632)Generalized Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,373,251)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 (4,703,540,875)PSA Double Bronze: Earned 100,000,000 credits (198,313,575)
Message 109834 - Posted: 2 Sep 2017 | 17:03:28 UTC
Last modified: 23 Sep 2017 | 11:58:42 UTC

On 29 August 2017, 14:15:23 UTC, PrimeGrid’s Generalized Fermat Prime Search found the Generalized Fermat mega prime:

919444^1048576+1

The prime is 6,253,210 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Fermat primes and 12th overall. This is the first Generalized Fermat prime found for n=20, the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime.

The discovery was made by Sylvanus A. Zimmerman (Van Zimmerman) of the United States using a Nvidia GeForce GTX 1060 in an Intel(R) Xeon(R) E3-1225 v3 CPU at 3.20GHz with 8GB RAM, running Microsoft Windows 10 Professional Edition. This GPU took about 4 hours 43 minutes to probable prime (PRP) test with GeneferOCL4. Sylvanus is a member of the Aggie The Pew team.

The prime was verified on 22 September 2017, 04:45:25 by Brian Konie (ScubaSteve) of the United States using an Intel(R) Xeon(R) E5-2620 CPU @ 2.00GHz with 16GB RAM, running Linux. This CPU took about 22 days, 13 hours, 25 minutes to probable prime (PRP) test with Genefer.

The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 16GB RAM, running Microsoft Windows 10 Professional Edition. This computer took about 3 days, 23 hours, 53 minutes to complete the primality test using multithreaded LLR.

For more details, please see the official announcement.

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Profile sergeProject donor
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Discovered 3 mega primesEliminated 2 conjecture "k"s321 LLR Turquoise: Earned 5,000,000 credits (5,342,838)Cullen LLR Silver: Earned 100,000 credits (158,983)ESP LLR Gold: Earned 500,000 credits (505,527)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,268,642)PPS LLR Emerald: Earned 50,000,000 credits (60,037,348)PSP LLR Silver: Earned 100,000 credits (120,541)SoB LLR Amethyst: Earned 1,000,000 credits (1,280,028)SR5 LLR Ruby: Earned 2,000,000 credits (2,649,390)SGS LLR Gold: Earned 500,000 credits (518,356)TRP LLR Silver: Earned 100,000 credits (141,131)Woodall LLR Silver: Earned 100,000 credits (116,405)Cullen/Woodall Sieve Silver: Earned 100,000 credits (235,088)PPS Sieve Amethyst: Earned 1,000,000 credits (1,031,526)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (500,445)TRP Sieve (suspended) Gold: Earned 500,000 credits (507,938)AP 26/27 Turquoise: Earned 5,000,000 credits (5,078,008)GFN Double Silver: Earned 200,000,000 credits (204,033,363)WW (retired) Ruby: Earned 2,000,000 credits (2,004,000)PSA Silver: Earned 100,000 credits (291,533)
Message 109845 - Posted: 2 Sep 2017 | 19:32:30 UTC

Extends https://oeis.org/A056993 (posted).

Congratulations!

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Profile JeppeSNProject donor
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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (684,183)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (112,799)PPS LLR Sapphire: Earned 20,000,000 credits (21,892,747)PSP LLR Gold: Earned 500,000 credits (598,093)SoB LLR Gold: Earned 500,000 credits (774,243)SR5 LLR Silver: Earned 100,000 credits (210,142)SGS LLR Silver: Earned 100,000 credits (142,930)TRP LLR Silver: Earned 100,000 credits (476,246)Woodall LLR Silver: Earned 100,000 credits (281,400)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)Cullen/Woodall Sieve Bronze: Earned 10,000 credits (22,952)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (52,559)GFN Ruby: Earned 2,000,000 credits (4,988,252)WW (retired) Jade: Earned 10,000,000 credits (13,756,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 109848 - Posted: 2 Sep 2017 | 19:45:34 UTC - in response to Message 109845.

Extends https://oeis.org/A056993 (posted).

Congratulations!


Yeah, that is something we have waited for for a long time.

Of course, there is the theoretical possibility that this is not the smallest n=20 generalized Fermat prime. The minimal base still in progress with n=20 appears to be 880342.

I know the number of candidates between 880342 and 919444 which have not been double-checked (or even successfully checked just once?) must be small.

/JeppeSN

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Discovered 2 mega primes2017 Tour de Primes highest prime score2017 Tour de Primes largest primeFound 2 primes in the 2019 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,439,173)Cullen LLR Gold: Earned 500,000 credits (903,764)ESP LLR Silver: Earned 100,000 credits (471,911)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (3,814,358)PPS LLR Turquoise: Earned 5,000,000 credits (6,315,694)PSP LLR Gold: Earned 500,000 credits (721,253)SoB LLR Ruby: Earned 2,000,000 credits (3,589,702)SR5 LLR Gold: Earned 500,000 credits (730,930)SGS LLR Gold: Earned 500,000 credits (895,300)TRP LLR Silver: Earned 100,000 credits (216,272)Woodall LLR Gold: Earned 500,000 credits (708,424)Generalized Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (294,367)PPS Sieve Double Bronze: Earned 100,000,000 credits (105,852,771)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (497,610)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (12,398,294)AP 26/27 Ruby: Earned 2,000,000 credits (4,055,129)GFN Emerald: Earned 50,000,000 credits (78,952,587)PSA Ruby: Earned 2,000,000 credits (2,292,938)
Message 109861 - Posted: 2 Sep 2017 | 22:30:55 UTC - in response to Message 109848.

Wow. Congratulations!!
____________

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HonzaProject donor
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Joined: 15 Aug 05
Posts: 1963
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Discovered 15 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 PrimesFound 4 primes in the 2021 Tour de PrimesFound 1 mega prime in the 2021 Tour de PrimesFound 1 prime in the 2021 Tour de Primes Mountain StageFound 2 primes in the 2022 Tour de PrimesFound 1 mega prime in the 2022 Tour de PrimesFound 3 primes in the 2023 Tour de PrimesFound 1 mega prime in the 2023 Tour de PrimesFound 1 prime in the 2023 Tour de Primes Mountain Stage321 LLR Double Bronze: Earned 100,000,000 credits (111,840,588)Cullen LLR Double Bronze: Earned 100,000,000 credits (118,233,898)ESP LLR Double Bronze: Earned 100,000,000 credits (100,642,296)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (106,956,296)PPS LLR Double Silver: Earned 200,000,000 credits (248,728,523)PSP LLR Double Bronze: Earned 100,000,000 credits (111,661,400)SoB LLR Double Bronze: Earned 100,000,000 credits (133,324,006)SR5 LLR Double Silver: Earned 200,000,000 credits (288,329,709)SGS LLR Double Bronze: Earned 100,000,000 credits (103,555,340)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Double Bronze: Earned 100,000,000 credits (131,874,357)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,172,892)321 Sieve (suspended) Double Bronze: Earned 100,000,000 credits (115,948,450)Cullen/Woodall Sieve Double Bronze: Earned 100,000,000 credits (100,408,718)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 (277,197,773)GFN Double Amethyst: Earned 1,000,000,000 credits (1,211,429,299)WW (retired) Double Ruby: Earned 2,000,000,000 credits (2,018,796,000)PSA Double Gold: Earned 500,000,000 credits (536,055,990)
Message 109926 - Posted: 4 Sep 2017 | 6:21:51 UTC

Congratilation, this is significant found.

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Message boards : News : GFN-1048576 Mega Prime!

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