PrimeGrid’s321 Prime Search
On 14 January 2014 15:26:41 UTC, PrimeGrid’s 321 Prime Search found another Mega
Prime:3*210829346+1
The prime is 3,259,959 digits long and will enter Chris Caldwell's “The Largest Known
Primes Database” (http://primes.utm.edu/primes) ranked 12th overall. This is the largest
known prime for the 3*2^n+1 form.
The discovery was made by Sai Yik Tang of Malaysia using an Intel(R) Core(TM) i5-2400
CPU @ 3.10GHz with 4 GB RAM running Windows 7 Enterprise x64. This computer tookabout 17 hours and 40 minutes to complete the primality test using LLR.
The prime was verified on 14 January 2014 20:23:24, by user schnabelt of Germany using
an Intel(R) Pentium(R) CPU G850 @ 2.90GHz with 4 GB RAM running Windows 7
Enterprise x64. This computer took about 22 hours and 47 minutes to complete the primality
test using LLR.
Credits for the discovery are as follows:
1.
2.
3.
4.

Sai Yik Tang (Malaysia), discoverer
PrimeGrid, et al.
Srsieve, sieving program developed by Geoff Reynolds
LLR, primality program developed by Jean Penne

Entry in “The Largest Know Primes Database” can be found here:
http://primes.utm.edu/primes/page.php?id=116922
OpenPFGW, a primality program developed by Chris Nash & Jim Fougeron, was used tocheck for Fermat Number divisibility (including generalized and extended). 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*2^10829346+1 is a Factor of GF(10829343,3)

3*2^10829346+1 is a Factor of xGF(10829344,9,8)

3*2^10829346+1 is a Factor of GF(10829345,5)

3*2^10829346+1 is a Factor of GF(10829345,11)

3*2^10829346+1 is a Factor of xGF(10829345,5,3)

3*2^10829346+1 is a Factor of xGF(10829345,11,3)

3*2^10829346+1 is a Factor of xGF(10829342,7,4)

3*2^10829346+1 is a Factor of xGF(10829344,11,5)

3*2^10829346+1 is a Factor of GF(10829344,8)

3*2^10829346+1 is a Factor of xGF(10829345,11,8)

3*2^10829346+1 is a Factor of xGF(10829344,8,3)

3*2^10829346+1 is a Factor of xGF(10829345,11,9)

3*2^10829346+1 is a Factor of xGF(10829345,8,5)

3*2^10829346+1 is a Factor of xGF(10829343,12,7)

3*2^10829346+1 is a Factor of xGF(10829345,9,5)Using a single core PC would have taken decades to find this prime. So this timely discovery
would not have been possible without the thousands of volunteers who contributed theirspare CPU cycles. A special thanks to everyone who contributed their advice and/or
computing power to the search.
The 321 Prime Search will continue to seek even larger primes. To join the search please
visit PrimeGrid: http://www.primegrid.com

PrimeGrid’s
321 Prime Search
About PrimeGrid
PrimeGrid is a distributed computing project, developed by Rytis Slatkevičius, Lennart Vogel,and John Blazek, which utilizes BOINC and PRPNet to search for primes. PrimeGrid'sprimary goal is to bring the excitement of prime finding to the "everyday" computer user.
Simply download the software and let your computer do the rest. Participants can choose
from a variety 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 a software
platform for distributed computing using volunteered computer resources. It allows
users to participate in multiple distributed computing projects through a single program.
Currently BOINC is being developed by a team based at the University of California,
Berkeley led by David Anderson.
This platform currently supports projects from biology to math to astronomy. For moreinformation, please visit BOINC: http://boinc.berkeley.edu
PRPNetPRPNet is a client/server application written by Mark Rodenkirch that is specificallydesigned to help find prime numbers of various forms. It is easily ported between
various OS/hardware combinations. PRPNet does not run each PRP test itself, butrelies on helper programs, such as LLR, PFGW, phrot, and genefer to do the work.
For more information, please visit PrimeGrid’s PRPNet forum thread:
http://www.primegrid.com/forum_thread.php?id=1215
For more information about PrimeGrid and a complete list of available prime search projects,
please visit: http://www.primegrid.com