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Message boards : News : World Record Generalized Cullen Prime!

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Scott BrownProject donor
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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 28 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 PrimesFound 8 primes in the 2021 Tour de PrimesFound 1 mega prime in the 2021 Tour de Primes321 LLR Double Silver: Earned 200,000,000 credits (201,403,028)Cullen LLR Double Silver: Earned 200,000,000 credits (201,409,561)ESP LLR Double Silver: Earned 200,000,000 credits (214,825,147)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (140,142,553)PPS LLR Double Gold: Earned 500,000,000 credits (736,184,727)PSP LLR Double Bronze: Earned 100,000,000 credits (199,380,197)SoB LLR Double Silver: Earned 200,000,000 credits (207,028,068)SR5 LLR Double Silver: Earned 200,000,000 credits (214,437,634)SGS LLR Double Silver: Earned 200,000,000 credits (205,718,935)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 Silver: Earned 200,000,000 credits (201,651,344)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 (2,732,435,721)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 (459,594,603)GFN Double Ruby: Earned 2,000,000,000 credits (2,152,607,365)WW Double Ruby: Earned 2,000,000,000 credits (2,667,896,000)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 151611 - Posted: 23 Sep 2021 | 15:16:52 UTC

On 28 August 2021, 09:10:17 UTC, PrimeGrid’s Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime:

2525532*732525532+1

Generalized Cullen numbers are of the form: n*bn+1. Generalized Cullen numbers that are prime are called Generalized Cullen primes. For more information, please see “Cullen prime” in The Prime Glossary.

The prime is 4,705,888 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Cullen primes and 24th overall.

Base 73 was one of 10 primeless Generalized Cullen bases for b ≤121 that PrimeGrid is searching. The remaining bases are 13, 29, 47, 49, 55, 69, 101, 109 & 121.

The discovery was made by Tom Greer (tng) of the United States using an Intel(R) Core(TM) i9-10920X CPU @ 3.50GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 10 hours, 40 minutes to complete the primality test using LLR2. Tom is a member of the Antarctic Crunchers team.

The prime was verified on 28 August 2021, 18:01 UTC, by an Intel(R) Core(TM) i7-9800X CPU @ 3.80GHz with 32GB of RAM, running CentOS. This computer took 3 hours and 39 minutes to complete the primality test using LLR2.

For more details, please see the official announcement.

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Message boards : News : World Record Generalized Cullen Prime!

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