PrimeGrid’s
Generalized Cullen/Woodall Prime Search
On 21 August 2017, 14:51:43 UTC, PrimeGrid’s Generalized Cullen/Woodall Prime Search foundthe largest known generalized Cullen prime:
1341174*53

1341174+1

Generalized Cullen numbers are of the form: n*b^n+1. Generalized Cullen numbers that are prime
are called generalized Cullen primes. For more information, please see “Cullen prime” in The PrimeGlossary (http://primes.utm.edu/glossary).

The prime is 2,312,561 digits long and enters Chris Caldwell's “The Largest Known PrimesstthDatabase” (http://primes.utm.edu/primes) ranked 1 for Generalized Cullen primes and 30overall.
The discovery was made by Hiroyuki Okazaki of Japan using an Intel(R) CPU @ 2.90GHz with
16GB RAM, running Linux. This computer took about 12 hours and 39 minutes to complete theprimality test using multithreaded LLR. Hiroyuki is a member of the Aggie The Pew team.
The prime was verified on 22 August 2017 17:24:17 UTC by user “wuzzat” of Australia using anIntel(R) Xeon(R) E5-2620 v3 CPU @ 2.40GHz with 256GB RAM, running Microsoft Windows
Server 2008R2. This computer took about 31 hours 41 minutes to complete the primality test
using LLR. “wuzzat” is a member of the BOINC@AUSTRALIA team.
The credits for the discovery are as follows:
1.
2.
3.
4.
5.

Hiroyuki Okazaki (Japan), discoverer
PrimeGrid, et al.
MultiSieve, sieve program developed by Mark Rodenkirch
gcwsieve, sieve program developed by Geoff Reynolds
LLR, primality program developed by Jean Penné

Entry in “The Largest Known Primes Database” can be found here:
http://primes.utm.edu/primes/page.php?id=123862
Base 53 was one of 14 prime-less generalized Cullen bases below b=121 that PrimeGrid issearching. The remaining bases are 13, 25, 29, 41, 47, 49, 55, 69, 73, 101, 109, 116 & 121.
Using a single PC would have taken years to find this prime. So this timely discovery would nothave 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 all the sievers who work behind the scenes to make a find like this possible.
PrimeGrid’s Generalized Cullen/Woodall Prime Search will continue seeking primes for otherprimeless bases. To join the search please visit PrimeGrid: http://www.primegrid.com

PrimeGrid’s
Generalized Cullen/Woodall Prime Search
About PrimeGrid
PrimeGrid is a distributed computing project, developed by Rytis Slatkevičius and currently
administered by Iain Bethune, James Breslin, Scott Brown, Ulrich Fries, Charley Gielkens,Michael Goetz, Roger Karpin, Rytis Slatkevičius, and Van Zimmerman.
PrimeGrid is hosted by Rackspace, and their generous contributions have helped make thisproject possible.
PrimeGrid utilizes BOINC and PRPNet to search for primes with the primary goal of bringing theexcitement of prime finding to the "everyday" computer user. Simply download the software andlet 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 even record 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 toparticipate in multiple distributed computing projects through a single program. CurrentlyBOINC is being developed by a team based at the University of California, Berkeley led byDavid Anderson.
This platform currently supports projects from biology to math to astronomy. For moreinformation, 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, but relies on helper
programs, such as LLR, PFGW, phrot, wwww, 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