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Message boards : News : PPS Mega Prime!

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Scott BrownProject donor
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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 12 mega primesEliminated 6 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 1 Fermat divisor2012 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 Stage321 LLR Double Bronze: Earned 100,000,000 credits (100,829,118)Cullen LLR Double Bronze: Earned 100,000,000 credits (103,870,990)ESP LLR Double Bronze: Earned 100,000,000 credits (103,603,483)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (102,075,655)PPS LLR Double Silver: Earned 200,000,000 credits (303,052,366)PSP LLR Emerald: Earned 50,000,000 credits (88,692,247)SoB LLR Double Bronze: Earned 100,000,000 credits (116,841,417)SR5 LLR Double Bronze: Earned 100,000,000 credits (129,423,098)SGS LLR Double Bronze: Earned 100,000,000 credits (148,139,564)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Bronze: Earned 100,000,000 credits (109,149,031)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,356,263)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,322,150)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve Double Silver: Earned 200,000,000 credits (240,468,300)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,105,665,691)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 Bronze: Earned 100,000,000 credits (119,533,830)GFN Double Gold: Earned 500,000,000 credits (902,983,417)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 59130 - Posted: 6 Nov 2012 | 2:19:51 UTC
Last modified: 6 Nov 2012 | 2:20:26 UTC

On 23 October 2012, PrimeGrid’s Proth Prime Search project found the Mega Prime:

9*2^3497442 +1

The prime is 1,052,836 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 51st overall. This prime is also a Generalized Fermat prime and ranks as the 12th largest found.

The discovery was made by Heinz Ming (parabol) of Switzerland using an Intel Core(TM) i7 CPU 860 @ 2.80GHz with 8GB RAM, running Windows 7 Professional. This computer took just over 5 hours 59 minutes to complete the primality test using LLR. Heinz Ming is a member of the Aggie The Pew team.

The prime was verified by Tim McArdle (Bauerwulf) of the United States using an AMD Athlon(tm) II P340 Dual-Core Processor with 6 GB RAM, running Windows 7 Professional. Jason is a member of the Don't Panic Labs team.

For more details, please see the official announcement.

Profile Gary Craig
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Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,614,439)Cullen LLR Ruby: Earned 2,000,000 credits (2,440,687)ESP LLR Turquoise: Earned 5,000,000 credits (5,019,435)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,029,174)PPS LLR Turquoise: Earned 5,000,000 credits (5,800,071)PSP LLR Turquoise: Earned 5,000,000 credits (5,000,433)SoB LLR Ruby: Earned 2,000,000 credits (4,087,062)SR5 LLR Turquoise: Earned 5,000,000 credits (5,040,727)SGS LLR Ruby: Earned 2,000,000 credits (3,142,971)TRP LLR Jade: Earned 10,000,000 credits (11,796,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,282,622)321 Sieve (suspended) Silver: Earned 100,000 credits (200,818)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (59,788,598)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,056,778)PPS Sieve Double Silver: Earned 200,000,000 credits (450,488,341)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 Gold: Earned 500,000 credits (530,229)GFN Double Bronze: Earned 100,000,000 credits (106,896,662)PSA Emerald: Earned 50,000,000 credits (62,378,755)
Message 59137 - Posted: 6 Nov 2012 | 8:18:58 UTC - in response to Message 59130.

The PDF "official announcement" has a typo (line 4). The exponent is wrong... it has an extra "9" at the start. Below, "Switzerland" is missing a vowel.

--Gary
(a.k.a Dr. Buzzkill)

Scott BrownProject donor
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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 12 mega primesEliminated 6 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 1 Fermat divisor2012 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 Stage321 LLR Double Bronze: Earned 100,000,000 credits (100,829,118)Cullen LLR Double Bronze: Earned 100,000,000 credits (103,870,990)ESP LLR Double Bronze: Earned 100,000,000 credits (103,603,483)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (102,075,655)PPS LLR Double Silver: Earned 200,000,000 credits (303,052,366)PSP LLR Emerald: Earned 50,000,000 credits (88,692,247)SoB LLR Double Bronze: Earned 100,000,000 credits (116,841,417)SR5 LLR Double Bronze: Earned 100,000,000 credits (129,423,098)SGS LLR Double Bronze: Earned 100,000,000 credits (148,139,564)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Bronze: Earned 100,000,000 credits (109,149,031)Woodall LLR Double Bronze: Earned 100,000,000 credits (101,356,263)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (8,322,150)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve Double Silver: Earned 200,000,000 credits (240,468,300)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,105,665,691)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 Bronze: Earned 100,000,000 credits (119,533,830)GFN Double Gold: Earned 500,000,000 credits (902,983,417)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 59171 - Posted: 6 Nov 2012 | 15:57:29 UTC - in response to Message 59137.


Thanks for the heads up on the errors. I had already fixed the extra "9", so you must have looked at it in the brief period after the news post and before the new pdf was uploaded. I'll add the "i" to Switzerland and get a new file up when I get home from work today.

And it looks like we have another PPS mega prime! News post forthcoming soon...this one is a bit bigger at about 1.7 million digits!

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321 LLR Silver: Earned 100,000 credits (399,839)Cullen LLR Gold: Earned 500,000 credits (606,597)ESP LLR Silver: Earned 100,000 credits (194,515)PPS LLR Silver: Earned 100,000 credits (232,494)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (178,947)PPS Sieve Double Gold: Earned 500,000,000 credits (749,714,906)AP 26/27 Silver: Earned 100,000 credits (413,909)GFN Ruby: Earned 2,000,000 credits (2,913,819)
Message 59177 - Posted: 6 Nov 2012 | 17:16:01 UTC
Last modified: 6 Nov 2012 | 17:16:23 UTC

This prime is also a Generalized Fermat prime and ranks as the 12th largest found


Maybe "... Generalized Fermat prime divisor ..."? :)
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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 (2,063,182)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 (7,371,106)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 (2,067,047)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 (3,672,652)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 (53,145,608)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 59178 - Posted: 6 Nov 2012 | 17:30:22 UTC - in response to Message 59177.

This prime is also a Generalized Fermat prime and ranks as the 12th largest found


Maybe "... Generalized Fermat prime divisor ..."? :)


Nope, it's also a GFN, not a divisor. :)

I'll leave it to the reader to search the boards for the explanation. The key is that 9 = 3^2.
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321 LLR Amethyst: Earned 1,000,000 credits (1,063,954)Cullen LLR Gold: Earned 500,000 credits (665,748)ESP LLR Amethyst: Earned 1,000,000 credits (1,025,432)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (374,632)PPS LLR Turquoise: Earned 5,000,000 credits (5,215,663)PSP LLR Amethyst: Earned 1,000,000 credits (1,134,556)SoB LLR Amethyst: Earned 1,000,000 credits (1,064,898)SR5 LLR Amethyst: Earned 1,000,000 credits (1,043,015)SGS LLR Amethyst: Earned 1,000,000 credits (1,072,821)TRP LLR Amethyst: Earned 1,000,000 credits (1,026,807)Woodall LLR Amethyst: Earned 1,000,000 credits (1,042,977)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,737)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,911,344)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,077,092)PPS Sieve Sapphire: Earned 20,000,000 credits (45,225,274)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,034,014)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,774)AP 26/27 Amethyst: Earned 1,000,000 credits (1,913,157)GFN Ruby: Earned 2,000,000 credits (4,084,085)PSA Sapphire: Earned 20,000,000 credits (47,256,391)
Message 59179 - Posted: 6 Nov 2012 | 18:03:12 UTC

I'm glad that our PPS work in high ranges turned out two primes, much better than turning out none. Now we just need to get a 321 prime from the challenge.
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321 LLR Silver: Earned 100,000 credits (399,839)Cullen LLR Gold: Earned 500,000 credits (606,597)ESP LLR Silver: Earned 100,000 credits (194,515)PPS LLR Silver: Earned 100,000 credits (232,494)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (178,947)PPS Sieve Double Gold: Earned 500,000,000 credits (749,714,906)AP 26/27 Silver: Earned 100,000 credits (413,909)GFN Ruby: Earned 2,000,000 credits (2,913,819)
Message 59481 - Posted: 13 Nov 2012 | 19:02:55 UTC
Last modified: 13 Nov 2012 | 19:05:28 UTC

Michael Goetz
Thank you :), but as I know, GFN has the form a^(2^n) + b^(2^n) (http://en.wikipedia.org/wiki/Fermat_number#Generalized_Fermat_numbers). This prime is 9 * 2^3497442 + 1 = 3^2 * 2^(2*3*13*44839) + 1. Does not seem at SomethingA^(2^SomethingB) + 1. Information in wiki about GFNs is not complete?

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Found 2 primes in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,570,600)Cullen LLR Turquoise: Earned 5,000,000 credits (5,098,443)ESP LLR Turquoise: Earned 5,000,000 credits (9,085,104)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (14,283,412)PPS LLR Turquoise: Earned 5,000,000 credits (9,277,645)PSP LLR Turquoise: Earned 5,000,000 credits (6,435,120)SoB LLR Turquoise: Earned 5,000,000 credits (7,584,477)SR5 LLR Turquoise: Earned 5,000,000 credits (5,890,852)SGS LLR Turquoise: Earned 5,000,000 credits (6,136,345)TPS LLR (retired) Bronze: Earned 10,000 credits (76,372)TRP LLR Turquoise: Earned 5,000,000 credits (7,767,011)Woodall LLR Turquoise: Earned 5,000,000 credits (8,281,303)321 Sieve (suspended) Silver: Earned 100,000 credits (209,833)Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,000,264)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (9,731,756)PPS Sieve Double Silver: Earned 200,000,000 credits (342,928,524)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,177,104)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,556,644)AP 26/27 Sapphire: Earned 20,000,000 credits (25,313,103)GFN Double Silver: Earned 200,000,000 credits (280,426,731)PSA Double Gold: Earned 500,000,000 credits (819,909,878)
Message 59482 - Posted: 13 Nov 2012 | 19:10:39 UTC - in response to Message 59481.
Last modified: 13 Nov 2012 | 19:11:15 UTC

9*2^3497442 +1
= 3^2 * (2^1748721)^2 +1
= (3*2^1748721)^2 +1
= (3*2^1748721)^(2^1) +1
;)
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