PrimeGridʼs
Generalized Cullen/Woodall Prime Search
On 24 Feb 2011, 17:27:31 UTC, PrimeGrid’s PRPNet found the largest known
generalized Woodall prime:

404882*43404882-1
Generalized Woodall numbers are of the form: n*b^n-1. Generalized Woodall numbers that are prime
are called generalized Woodall primes. For more information, please see “Woodall prime” in The
Prime Glossary (http://primes.utm.edu/glossary).

The prime is 661,368 digits long and enters Chris Caldwell's “The Largest Known Primes
Database” (http://primes.utm.edu/primes) ranked 1st for generalized Woodall primes and71st 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 Athlon
II X4 635 @ 2.90GHz with 8GB RAM, running Windows 7. This computer took about 4hours and 15 minutes to complete the probable prime test using pfgw64. The same
computer took a little over 30 hours 3 minutes to complete the primality test using
pfgw64. Ricky is a member of the AMD Users Team.
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

Entry in “The Largest Know Primes Database” can be found here:
http://primes.utm.edu/primes/page.php?id=98862
Base 43 was the lowest base without a generalized Woodall prime although it had beentested further than any other generalized base. Now it stands out with producing thelargest known generalized Woodall prime.
Using a single PC would have taken years to find this prime. So this timely discovery
would not have been possible without the 140 plus 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, which
utilizes BOINC and PRPNet to search for primes. PrimeGrid's primary goal is to bring theexcitement of prime finding to the "everyday" computer user. Simply download thesoftware and let your computer do the rest. Participants can choose from a variety ofprime forms to search. With a little patience, you may find a large or even record
breaking prime.
BOINCThe 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, 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