PrimeGridʼs
Generalized Cullen/Woodall Prime Search
On 29 Jan 2012, 08:10:03 UTC, PrimeGrid’s PRPNet found the largest known
generalized Cullen prime:

427194*113427194+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 Prime
Glossary (http://primes.utm.edu/glossary).

The prime is 877,069 digits long and enters Chris Caldwell's “The Largest Known Primes
Database” (http://primes.utm.edu/primes) ranked 1st for generalized Cullen primes and57th overall. It is the largest non-base 2/non-generalized Fermat prime ever found.
The discovery was made by Ricky L. Hubbard of the United States using an AMD
Phenom II X6 1090t @ 3.2GHz with 8GB RAM, running Windows 7. This computer took
7 hours and 15 minutes to complete the probable prime test using pfgw64 and 7 hours
20 minutes to complete the primality test again using pfgw64. Ricky is a member of theAMD Users Team.
Ricky has the special distinction of also holding the record for the largest generalized
Woodall prime: 404882*43^404882-1.
The credits for the discovery are as follows:
1.
2.
3.
4.
5.

Ricky L. Hubbard (United States), discoverer
PrimeGrid, et al.
MultiSieve, sieve program developed by Mark Rodenkirch
gcwsieve, sieve program developed by Geoff Reynolds
PFGW, primality program developed by Chris Nash & Jim Fougeron withmaintenance and improvements by Mark Rodenkirch

Entry in “The Largest Know Primes Database” can be found here:
http://primes.utm.edu/primes/page.php?id=104121
Base 113 was one of 16 prime-less generalized Cullen bases below b=121 thatPrimeGrid is searching. The remaining bases are 13, 25, 29, 41, 47, 49, 53, 55, 69, 73,79, 101, 109, 116 & 121. All have been extensively searched so this find is very exciting.
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 Mark Rodenkirch, Steven Harvey, andLennart Vogel who were instrumental in moving the project forward and to all thePRPNet’ers who contributed to this effort.
PrimeGrid’s Generalized Cullen/Woodall Prime Search will continue seeking primes forother primeless bases. To join the search please visit PrimeGrid:
http://www.primegrid.com

PrimeGridʼsGeneralized Cullen/Woodall 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's primary 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 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 to participate in multiple distributed computing projects through a singleprogram. 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. Formore information, 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, 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