[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-prime-rules.php


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/source.htm

 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.sdstate.edu/~fib/.  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/