PrimeGrid’s
Generalized Fermat Prime Search
On 14 December 2018, 07:07:34 UTC, PrimeGrid’s Generalized Fermat Prime Searchfound the Generalized Fermat mega prime:
6291332262144+1
The prime is 1,782,250 digits long and enters Chris Caldwell's “The Largest Known
Primes Database” (http://primes.utm.edu/primes) ranked 10th for Generalized Fermat
primes and 66th overall.
The discovery was made by Karsten Freihube of Germany using an NVIDIA GeForceGTX 1060 in an Intel(R) Core(TM) i7-4790 CPU at 3.60GHz with 16GB RAM, running
Windows 10 Proffesional Edition. This GPU took about 35 minutes to probable prime(PRP) test with GeneferOCL2.
The prime was verified on 14 December 2018, 14:47:41 by Andreas Zenker of Austria
Republic using an NVIDIA GeForce GTX 1060 GPU in an Intel(R) Core(TM)2 Quad CPU
at 2.50GHz 4GB RAM, running Windows 7 Professional Edition. This GPU took about
42 minutes to probable prime (PRP) test with GeneferOCL2. Andreas is a member ofTeam PC-Reflate.
The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with
16GB RAM, running Microsoft Windows 10 Professional. This computer took about 4hours 59 minutes to complete the primality test using LLR.
The credits for the discovery are as follows:
1.
2.
3.
4.
5.
6.

Karsten Freihube (Germany), discoverer
PrimeGrid, et al.
AthGFNSieve, sieve program developed by David Underbakke
GFNSvCUDA, sieve program developed by Anand Nair
GeneferOCL, probable prime program developed by Yves Gallot
LLR, primality program developed by Jean Penné

Entry in “The Largest Known Primes Database” can be found here:
https://primes.utm.edu/primes/page.php?id=125862
Using a single PC would have taken years to find this prime. So this timely discovery
would not have been possible without the hundreds of volunteers who contributed theirspare CPU cycles. A special thanks to everyone who offered their advice and/or
computing power to the search - especially Yves Gallot, Iain Bethune, DavidUnderbakke, Anand Nair, Mark Rodenkirch and Geoff Reynolds who were major forcesin moving the project forward. Also, thank you to all the sievers, especially Honza Cholt
and Jim Breslin. A final thanks to Michael Goetz for porting to BOINC.
The Generalized Fermat Prime Search will continue to seek even larger primes. To join
the search please visit PrimeGrid: http://www.primegrid.com

PrimeGrid’s
Generalized Fermat Prime Search
About PrimeGrid
PrimeGrid is a distributed computing project, developed by Rytis Slatkevičius andcurrently managed by Iain Bethune, James Breslin, Scott Brown, Ulrich Fries, MichaelGoetz, Roger Karpin, Rytis Slatkevičius, and Van Zimmerman.
PrimeGrid utilizes BOINC and PRPNet to search for primes with the primary goal ofbringing the excitement of prime finding to the "everyday" computer user. Simplydownload 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 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 ofCalifornia, 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 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, wwww, and genefer to dothe 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
projects, please visit: http://www.primegrid.com