M48

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M48
Prime class :
Type : Mersenne prime
Formula : Mn = 2n - 1
Prime data :
Rank : 48 (Provisional ranking)
n-value : 57,885,161
Number : 581887266232...071724285951
Digits : 17,425,170
Perfect number : 257,885,160 • (257,885,161-1)
Digits : 34,850,340
Discovery data :
Date of Discovery : 2013-01-25
Discoverer : Curtis Cooper
Found with : Lucas-Lehmer test
Prime95 on Intel Core2 Duo E8400 @ 3.00GHz
Credits : George Woltman
Scott Kurowski
Aaron Blosser et. al.
(GIMPS & PrimeNet)

M48 normally refers to the 48th Mersenne prime, in order of size from the smallest to greatest. This is the primary usage and what is referred to in the rest of this article. For clarification about other possible usages refer to the Nomenclature and notation article.

Discovery

The official discovery date for 257,885,161-1 was 2013-01-25. See the press release for the full description of this discovery.

Verification

To confirm that there were no errors in the hardware or software, the number had to be independently verified by running tests on various machines with different architecture and software.

The volunteers that ran these tests were:

  • Serge Batalov, who ran Ernst Mayer's Mlucas software on a 32 core server for 6 days (resource donated by Novartis IT group)
  • Jerry Hallett, who ran CUDALucas on an NVIDIA GPU for 3.6 days
  • Dr. Jeff Gilchrist, who ran two separate tests:
    • GIMPS software on an Intel i7 CPU for 4.5 days
    • CUDALucas software on an NVIDIA GTX 560 Ti in 7.7 days

External links