PrimeGridʼs
Generalized Woodall Prime Search
On 07 Dec 2009, 08:32:59 UTC, PrimeGrid’s PRPNet found the largest known
generalized Woodall prime:563528*13563528-1
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 627,745 digits long and enters Chris Caldwell's “The Largest Known Primes
Database” (http://primes.utm.edu/primes) ranked 1st for generalized Woodall primes and65th overall. It is the largest non-base 2/non-generalized Fermat prime ever found.
The discovery was made by Lennart Vogel of Sweden using an Intel Q6600 @ 2.4 GHzwith 4 GB RAM. This computer took about 3 hours and 54 minutes to complete theprobable prime test using pfgw. Lennart is a member of the PrimeSearchTeam.
The prime was confirmed on 08 Dec 2009, 16:04:00 UTC, by an Intel Q6600 @ 2.4 GHzwith 4 GB RAM. This computer took a little over 30 hours 3 minutes to complete theprimality test using pfgw.
The credits for the discovery are as follows:
1.
2.
3.
4.
5.

Lennart Vogel (Sweden), 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=91121
Base 13 had the peculiarity of having no generalized Cullen or Woodall primes although
it had been tested further than any other generalized base. This disparity certainly made13 very 'unlucky'. However, its fate has changed now producing the largest 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 almost 50 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 and Lennart Vogel who
were major forces in moving the project forward and to all the PRPNet’ers whocontributed to this effort.
PrimeGrid’s Generalized Woodall Prime Search is now complete for base 13. However,
the Cullen side will continue up to 1M or until a prime is found. To join the search please
visit PrimeGrid: http://www.primegrid.com

PrimeGridʼsGeneralized 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.
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. 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