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On 11 Aug 2008, 6:32 UTC, PrimeGrid's 321 Prime Search
found its first prime.
The discovery was made by Thomas Wolfram of Germany using
an Intel Pentium M @ 1.6 GHz with 512 MB RAM running
Windows 2000.
The prime was verified on 13 August 2008 12:06 UTC, by
Dale Laluk of Canada using an Intel Pentium 4 @ 3.0 GHZ
with 512 MB RAM running Windows XP.
Generalized and extended generalized Fermat Divisors
discovered by Lennart Vogel are as follows (using the
following settings in PFGW: -gxo -a2 3*2^2291610+1):
3*2^2291610+1 is a Factor of GF(2291607,3)
3*2^2291610+1 is a Factor of GF(2291609,5)
3*2^2291610+1 is a Factor of xGF(2291609,5,3)
3*2^2291610+1 is a Factor of xGF(2291607,7,4)
3*2^2291610+1 is a Factor of GF(2291608,8)
3*2^2291610+1 is a Factor of xGF(2291608,8,3)
3*2^2291610+1 is a Factor of xGF(2291609,8,5)
3*2^2291610+1 is a Factor of xGF(2291609,9,5)
3*2^2291610+1 is a Factor of xGF(2291608,9,8)
3*2^2291610+1 is a Factor of GF(2291608,11)
3*2^2291610+1 is a Factor of xGF(2291608,11,3)
3*2^2291610+1 is a Factor of xGF(2291609,11,5)
3*2^2291610+1 is a Factor of xGF(2291607,11,8)
3*2^2291610+1 is a Factor of xGF(2291608,11,9)
3*2^2291610+1 is a Factor of xGF(2291604,12,7)
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 Lennart Vogel for doing
all the sieve work.
PrimeGrid's 321 Prime Search will continue to search for
even larger primes. To join the search please visit
PrimeGrid: www.primegrid.com
About PrimeGrid
Rytis Slatkevicius, the developer of PerlBOINC - a
Perl-language-based port of the BOINC platform, created
PrimeGrid as a test project for PerlBOINC. PrimeGrid's
first sub-project was in cryptography as it participated in
the RSA Factoring Challenge. While it no longer
participates in the challenge, PrimeGrid continues to
expand its functionality. Currently the project is running
the following sub-projects:
- Twin Prime Search: searching for gigantic twin primes
of the form k*2^n + 1 and k*2^n - 1.
- Cullen-Woodall Search: searching for mega primes of
forms n*2^n + 1 and n*2^n - 1.
- 321 Prime Search: searching for mega primes of the
form 3*2^n + 1 and 3*2^n - 1.
- Prime Sierpinski Project: helping Prime Sierpinski
Project solve the Prime Sierpinski Problem.
- Proth Prime Search: searching for primes of the form
k*2^n + 1.
For more information, please visit PrimeGrid: www.primegrid.com
About 321 Search
321 Search began in February 2003 from a post by Paul
Underwood seeking help from interested parties in a prime
search attempt of the form 3*2^n-1. The initial goal was
to build upon the completed work at Proth Search and extend
the list of known primes to an exponent of 1 million.
Interests gathered quickly and by the time they reached
n=1 million, they had already pre-sieved further.
Computer hardware advances allowed them to reach tests at
1 million digits or exponent of about 3.3 million within
a few years, with stated aim of eventually finding a
mega-prime.
321 Search successfully found a Mega Prime on 23 March
2008, 3*2^4235414-1. They completed their search and
stopped at n=5M. The project was archived on 22 September
2008 after a successful 5 1/2 year run.
For more information, please visit 321 Search: www.mersenneforum.org/321search/.
About BOINC
BOINC (Berkeley Open Infrastructure for Network
Computing) 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 of
California, Berkeley led by David Anderson.
For more information, please visit BOINC: boinc.berkeley.edu
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