PrimeGrid’s
Generalized Cullen/Woodall Prime Search
On 8 October 2016, 21:01:14 UTC, PrimeGrid’s PRPNet found the largest known
generalized Cullen prime:

682156*79682156+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 1,294,484 digits long and enters Chris Caldwell's “The Largest Known
Primes Database” (http://primes.utm.edu/primes) ranked 1st for generalized GeneralizedCullen and Generalized Cullen-Woodall primes and 83rd overall.
The discovery was made by Franz-Xaver Harvanek of Austria using an Intel(R)Core(TM) i7-5960X CPU @ 3.00GHz with 32GB RAM, running Microsoft Windows 7
Ultimate. This computer took 3 hours and 44 minutes to complete the primality test
using LLR.
The credits for the discovery are as follows:
1.
2.
3.
4.
5.

Franz-Xaver Harvanek (Austria), 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=122349
Base 79 was one of 15 prime-less generalized Cullen bases below b=121 thatPrimeGrid is searching. The remaining bases are 13, 25, 29, 41, 47, 49, 53, 55, 69, 73,101, 109, 116 & 121.
Using a single PC would have taken years to find this prime. So this timely discovery
would not have been possible without the thousands of volunteers who contributed theirspare CPU cycles. A special thanks to everyone who contributed their advice and/orcomputing power to the search, to all the PRPNet’ers who contributed to this effort, andespecially to 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 forother primeless bases. To join the search please visit PrimeGrid:
http://www.primegrid.com

PrimeGrid’sGeneralized 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. 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 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