PrimeGrid’s321 Prime Search
On 3 Apr 2009 15:40:01 UTC, PrimeGrid’s 321 Prime Search found another Mega
Prime:3*25082306+1
The prime is 1,529,928 digits long and will enter Chris Caldwell's “The Largest
Known Primes Database” (http://primes.utm.edu/primes) ranked 15th overall. It is
the 6th largest Proth prime found and the largest found Mega Prime using LLR.
The discovery was made by Andy Brady of the United States using an Intel C2Q
Q8200 @ 2.33GHz with 3GB RAM running Windows Vista. This computer took about
14 hours 7 minutes to complete the primality test. Andy is a member of theBOINCstats team.
The prime was verified on 4 Apr 2009 11:59:13 UTC, by Bogdan Lewdański ofPoland using an Intel C2Q Q6600 @ 2.40GHz with 3GB RAM running Windows XP.
This computer took about 8 hours 5 minutes to complete the primality test. Bogdan
is a member of the BOINC@Poland team.
The credits for the discovery are as follows:

1.
2.
3.
4.

Andy Brady (United States), discoverer
PrimeGrid, et al.
Srsieve, sieving program developed by Geoff Reynolds
LLR, primality program developed by Jean Penné

Entry in “The Largest Know Primes Database” can be found here:
http://primes.utm.edu/primes/page.php?id=87449
OpenPFGW, a primality program developed by Chris Nash & Jim Fougeron, was used
to check for Fermat Number divisibility (including generalized and extended) using
the following settings: -gxo –a2 3*25082306+1. For more information about Fermat
and Generalized Fermat Number divisors, please see Wilfrid Keller's sites:••

http://www.prothsearch.net/fermat.html
http://www1.uni-hamburg.de/RRZ/W.Keller/GFNfacs.html

Generalized and extended Generalized Fermat Number divisors discovered are as
follows:
3*2^5082306+1 is a Factor of GF(5082303,3)
3*2^5082306+1 is a Factor of GF(5082305,5)
3*2^5082306+1 is a Factor of xGF(5082305,5,3)
3*2^5082306+1 is a Factor of xGF(5082302,7,4)
3*2^5082306+1 is a Factor of GF(5082304,8)
3*2^5082306+1 is a Factor of xGF(5082304,8,3)
3*2^5082306+1 is a Factor of xGF(5082305,8,5)
3*2^5082306+1 is a Factor of xGF(5082305,9,5)

3*2^5082306+1 is a Factor of xGF(5082304,9,8)
3*2^5082306+1 is a Factor of GF(5082305,11)
3*2^5082306+1 is a Factor of xGF(5082305,11,3)
3*2^5082306+1 is a Factor of xGF(5082302,11,5)
3*2^5082306+1 is a Factor of xGF(5082305,11,8)
3*2^5082306+1 is a Factor of xGF(5082305,11,9)
3*2^5082306+1 is a Factor of xGF(5082303,12,7)

PrimeGrid’s
321 Prime Search
PrimeGrid’s 321 Prime Search is an extension of Paul Underwood’s 321 Searchwhich concluded at n=5M. PrimeGrid added the 3*2n+1 form to the search and is
testing both 3*2n-1 and 3*2n+1 forms beyond 5M.
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 whocontributed their spare CPU cycles. A special thanks to everyone who contributed
their advice and/or computing power to the search - especially Wilfrid Keller, the (x)(G)FN divisibility testers, and all the sievers who work behind the scenes to make afind like this possible.
PrimeGrid’s 321 Prime Search will continue to search for even larger primes. To join
the search please visit PrimeGrid: http://www.primegrid.com
About PrimeGrid
PrimeGrid is a distributed computing project, developed by Rytis Slatkevičius, which
utilizes BOINC and PRPNet to search for primes. PrimeGrid's primary goal is to bringthe excitement of prime finding to the "everyday" computer user. Simply download
the software and let your computer do the rest. Participants can choose from avariety of prime forms to search. With a little patience, you may find a large or evenrecord breaking prime.
BOINC
The Berkeley Open Infrastructure for Network Computing (BOINC) is asoftware platform for distributed computing using volunteered computerresources. It allows users to participate in multiple distributed computing
projects through a single program. Currently BOINC is being developed by ateam based at the University of California, Berkeley led by David Anderson.
This platform currently supports projects from biology to math to astronomy.
For more information, please visit BOINC: http://boinc.berkeley.edu
PRPNet
PRPNet is a distributed Client/Server application, developed by MarkRodenkirch, which can be used to manage and perform primality andprobable prime tests on a list of candidate numbers. The PRPNet Client uses
LLR, Phrot, or PFGW to perform these tests.
For more information and a list of the all available prime search projects, please
visit PrimeGrid: http://www.primegrid.com