PrimeGrid’s27121 Prime Search
On 11 October 2018, 22:54:34, PrimeGrid’s 27121 Prime Search, through PRPNet andin collaboration with the 12121 Search (k=27 sister project), has found the mega prime:
27*27046834+1
The prime is 2,121,310 digits long and will enter Chris Caldwell's “The Largest Known
Primes Database” (http://primes.utm.edu/primes) ranked 48th overall.
The discovery was made by Andrew M. Farrow of Australia using an Intel(R) Xeon(R)CPU E3-1245 v6 @ 3.70GHz Processor with 16GB RAM, running Linux. This
computer took about 1 hour 13 minutes to complete the primality test using LLR.
The prime was verified internally.
Credits for the discovery are as follows:
1.
2.
3.
4.
5.

Andrew M. Farrow (Australia), discoverer
PrimeGrid, et al.
Srsieve, sieving program developed by Geoff Reynolds
PSieve, sieving program developed by Ken Brazier and Geoff Reynolds
LLR, primality program developed by Jean Penné

Entry in “The Largest Known Primes Database” can be found here:
https://primes.utm.edu/primes/page.php?id=125683
PrimeGrid’s 27121 Prime Search is a collaboration with the 12121 Search, which wasestablished on 5/24/2004 to search for large primes of the form 121*2^n-1. Later, on
3/1/2005, they added k=27 to their search. Their "short term" goal is to search for n up
to 10M. PrimeGrid added the +1 form and searches both k’s and forms together.
Fermat number divisibility (including generalized and extended) was checked by
OpenPFGW using the following settings: -gxo -q27*2^7046834+1. For more
information about Fermat and generalized Fermat number divisors, please see Wilfrid
Keller's sites:• http://www.prothsearch.com/fermat.html• http://www.prothsearch.com/GFNfacs.html
Generalized and extended generalized Fermat number divisors are as follows:
27*2^7046834+1 is a Factor of xGF(7046830,10,3)
27*2^7046834+1 is a Factor of xGF(7046832,11,5)
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
their spare 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 thescenes to make a find like this possible.
The 27121 Prime Search will continue to seek even larger primes. To join the searchplease visit PrimeGrid: http://www.primegrid.com

PrimeGrid’s
27121 Prime Search
About PrimeGrid
PrimeGrid is a distributed computing project, developed by Rytis Slatkevičius andcurrently managed by Iain Bethune, James Breslin, Scott Brown, Ulrich Fries, MichaelGoetz, 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 froma variety 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 asingle program. Currently BOINC is being developed by a team based at theUniversity of California, 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
specifically designed 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, but relies 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