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Mersenne Research, Inc.'s 2009 claim for 243112609-1

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Mersenne Research, Inc.'s 2009 claim for 243112609-1

[This is the successful claim for EFF's $100,000 Cooperative Computing Award by Mersenne Research, Inc. This claim has been accepted by the Cooperative Computing Advisory Panel and the EFF Board of Directors.]

Dear Sirs,

Mersenne Research, Inc. is pleased to submit this claim for the $100,000 Electronic Frontier Foundation Cooperative Computing Award for discovery of a ten million digit prime number. Mersenne Research, Inc., a non-profit charitable research corporation, runs the Great Internet Mersenne Prime Search (GIMPS).

The following information should satisfy the requirements outlined in section 4 of your official rules at http://w2.eff.org/awards/coop...

Regards,
George Woltman and Scott Kurowski
President and Executive V.P. Mersenne Research, Inc.

4A. The prime number is 2^43,112,609-1. This number is the 45th known Mersenne prime consisting of 12,978,189 decimal digits.

4B. Primality was proved using the Lucas-Lehmer primality test for Mersenne numbers.

The number was pre-screened for factors below 2^68. The number was also pre-screened using P-1 factoring algorithm with a bound of 720,000.

4C. The number was found on a Dell Optiplex 745 computer with an Intel Core 2 Duo E6600 CPU running at 2.4 GHz.

The computer is owned by the University of California Los Angeles (UCLA) Mathematics Department. Edson Smith maintains the department's computers and installed the GIMPS client software to put the department's idle computer cycles to good use, participating in GIMPS under automated Internet server-directed control. The software used to conduct the Lucas-Lehmer test was version 24 of GIMPS' Prime95 client software written by George Woltman and Scott Kurowski. The source code is available at http://www.mersenne.org/sourc...

4D. The Lucas-Lehmer test began on Sun Jul 20 12:33:46 2008 PDT and concluded on Sat Aug 23 00:29:27 2008 PDT. That's a total of 33 1/2 days. The Dell Optiplex was the only computer used to initially prove this candidate prime. However, the computer was part of GIMPS' "PrimeNet" network of roughly 75,000 computers testing other Mersenne number candidates.

4E. The UTC time for the discovery was August 23, 2008, 08:29:27.

The number was verified as prime by independent parties, each party employing different hardware and software.

Tom Duell and Rob Giltrap at Sun Microsystems used the publicly available Mlucas program by Ernst Mayer. The verifications ran on a Sun SPARC Enterprise M5000 Server in Menlo Park, CA. The prime verification took 13 days.

The prime was also independently verified by Tony Reix of Bull SAS in Grenoble, France using a Bull NovaScale 6160 HPC server and the publicly available Glucas program by Guillermo Ballester Valor. Jeff Gilchrist of Carleton University in Ottawa, Canada has also verified the prime using a server at SHARCNET running the same software.

4F. The discovery has been published in the August 2009 issue of The Fibonacci Quarterly, a refereed journal.

The reference for the article is:
G. Woltman and S. Kurowski, "On the Discovery of the 45th and 46th Known Mersenne Primes."
The Fibonacci Quarterly, 46/47(2009):194-197

The abstract is as follows:

*Abstract. The Great Internet Mersenne Prime Search (GIMPS) has been coordinating a rigorous search for new Mersenne Prime discoveries. This paper provides a quick overview of Mersenne prime history, discusses the methods used by GIMPS to discover new primes, and presents the latest search results including two new Mersenne primes, M43112609 and M37156667 .*

The web address for the journal is http://www.engineering.sdstat.... The web site is not up-to-date.
If you do not have access to this journal, we can ask for permission to send a copy of the article.

4G. The point of contact is:

Scott Kurowski
Executive V.P., Mersenne Research, Inc.
[Contact information removed]

The URL for Mersenne Research, Inc is http://www.mersenne.org/

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