PrimeGrid’s
Generalized Cullen/Woodall Prime Search
On 11 March 2018, 23:54:40 UTC, PrimeGrid’s Generalized Cullen/Woodall PrimeSearch found the largest known Generalized Cullen prime:
1806676*411806676+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/xpage/Cullens.html).
The prime is 2,913,785 digits long and enters Chris Caldwell's “The Largest Known
Primes Database” (http://primes.utm.edu/primes) ranked 1st for Generalized Cullen
primes and 27th overall.
Base 41 was one of 12 prime-less Generalized Cullen bases below b=121 thatPrimeGrid is searching. The remaining bases are 13, 25, 29, 47, 49, 55, 69, 73, 101,
109 & 121.
The discovery was made by Hiroyuki Okazaki of Japan using an Intel(R) Xeon(R) E52670 CPU @ 2.60GHz with 4GB RAM, running Linux. This computer took about 7 hours
and 13 minutes to complete the primality test using multithreaded LLR. Hiroyuki is amember of the Aggie The Pew team.
The prime was verified on 12 March 2018 09:07:23 UTC by Scott Brown of the UnitedStates using an Intel(R) CPU @ 2.30GHz with 16GB RAM, running Windows 10
Professional Edition. This computer took about 15 hours 22 minutes to complete theprimality test using LLR. Scott is also a member of the Aggie The Pew 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=124515
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/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 forother primeless 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 andcurrently administered by Iain Bethune, James Breslin, Scott Brown, Ulrich Fries,Michael Goetz, Roger Karpin, Rytis Slatkevičius, and Van Zimmerman.
PrimeGrid utilizes BOINC and PRPNet to search for primes with the primary goal ofbringing 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 avariety of prime forms to search. With a little patience, you may find a large or evenrecord 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 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.