Proof-code: L753 (Another of the Prime Pages' resources)
Samuel Yates began, and this site continues, a database of the largest known primes. Primes in that database are assigned a proof-code to show who should be credited with the discovery as well as what programs and projects they used. (Discoverers have one prover-entry, but may have many proof-codes because they use a variety of programs...) This page provides data on L753, one of those codes.

 Code name (*): L753   (See the descriptive data below.) Persons (*): 1 (counting humans only) Projects (*): 1 (counting projects only) Display (HTML): Wolfram, Srsieve, PrimeGrid, LLR Number of primes: total 1 Unverified Primes: 0 (prime table entries marked 'Composite','Untested', or 'InProcess') Score for Primes (*): total 45.4935, on current list 45.4935 (normalized score 5) Entrance Rank (*): mean 40.00 (minimum 40, maximum 40)

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On 11 Aug 2008, 6:32 UTC, PrimeGrid's 321 Prime Search found its first prime.

The discovery was made by Thomas Wolfram of Germany using an Intel Pentium M @ 1.6 GHz with 512 MB RAM running Windows 2000.

The prime was verified on 13 August 2008 12:06 UTC, by Dale Laluk of Canada using an Intel Pentium 4 @ 3.0 GHZ with 512 MB RAM running Windows XP.

Generalized and extended generalized Fermat Divisors discovered by Lennart Vogel are as follows (using the following settings in PFGW: -gxo -a2 3*2^2291610+1):

3*2^2291610+1 is a Factor of GF(2291607,3)
3*2^2291610+1 is a Factor of GF(2291609,5)
3*2^2291610+1 is a Factor of xGF(2291609,5,3)
3*2^2291610+1 is a Factor of xGF(2291607,7,4)
3*2^2291610+1 is a Factor of GF(2291608,8)
3*2^2291610+1 is a Factor of xGF(2291608,8,3)
3*2^2291610+1 is a Factor of xGF(2291609,8,5)
3*2^2291610+1 is a Factor of xGF(2291609,9,5)
3*2^2291610+1 is a Factor of xGF(2291608,9,8)
3*2^2291610+1 is a Factor of GF(2291608,11)
3*2^2291610+1 is a Factor of xGF(2291608,11,3)
3*2^2291610+1 is a Factor of xGF(2291609,11,5)
3*2^2291610+1 is a Factor of xGF(2291607,11,8)
3*2^2291610+1 is a Factor of xGF(2291608,11,9)
3*2^2291610+1 is a Factor of xGF(2291604,12,7)

Using a single PC would have taken years to find this prime. So this timely discovery would not have been possible without the thousands of volunteers who contributed their spare CPU cycles. A special thanks to everyone who contributed their advice and/or computing power to the search - especially Lennart Vogel for doing all the sieve work.

PrimeGrid's 321 Prime Search will continue to search for even larger primes. To join the search please visit PrimeGrid: www.primegrid.com

Rytis Slatkevicius, the developer of PerlBOINC - a Perl-language-based port of the BOINC platform, created PrimeGrid as a test project for PerlBOINC. PrimeGrid's first sub-project was in cryptography as it participated in the RSA Factoring Challenge. While it no longer participates in the challenge, PrimeGrid continues to expand its functionality. Currently the project is running the following sub-projects:
• Twin Prime Search: searching for gigantic twin primes of the form k*2^n + 1 and k*2^n - 1.
• Cullen-Woodall Search: searching for mega primes of forms n*2^n + 1 and n*2^n - 1.
• 321 Prime Search: searching for mega primes of the form 3*2^n + 1 and 3*2^n - 1.
• Prime Sierpinski Project: helping Prime Sierpinski Project solve the Prime Sierpinski Problem.
• Proth Prime Search: searching for primes of the form k*2^n + 1.

321 Search began in February 2003 from a post by Paul Underwood seeking help from interested parties in a prime search attempt of the form 3*2^n-1. The initial goal was to build upon the completed work at Proth Search and extend the list of known primes to an exponent of 1 million. Interests gathered quickly and by the time they reached n=1 million, they had already pre-sieved further. Computer hardware advances allowed them to reach tests at 1 million digits or exponent of about 3.3 million within a few years, with stated aim of eventually finding a mega-prime.

321 Search successfully found a Mega Prime on 23 March 2008, 3*2^4235414-1. They completed their search and stopped at n=5M. The project was archived on 22 September 2008 after a successful 5 1/2 year run.