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M40
M40 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 40 |
n-value : | 20,996,011 |
Number : | 125976895450...762855682047 |
Digits : | 6,320,430 |
Perfect number : | 2^{20,996,010} • (2^{20,996,011}-1) |
Digits : | 12,640,858 |
Discovery data : | |
Date of Discovery : | 2003-11-17 |
Discoverer : | Michael Shafer |
Found with : | Lucas-Lehmer test / Prime95 on 2 GHz Dell Dimension |
Credits : | George Woltman et. al. GIMPS |
M40 is the short hand used to refer to the 40th Mersenne prime. Specifically it is 2^{20,996,011}-1. This number was discovered to be prime on 2003-11-17 by Michael Shafer, using Prime95 written by George Woltman. The number is 6,320,430 decimal digits long. This prime number was the sixth record prime found by the GIMPS project.
The discovery took 19 days of computation on a 2 GHz Pentium 4 Dell Dimension PC at a Michigan State University lab.
It was independently verified by Guillermo Ballester Valor of Granada, Spain (author of program Glucas) using twelve days of time on a 1.4GHz quad Itanium II server at the HP Test Drive center, and by Ernst Mayer of Cupertino, California (author of program Mlucas) using three weeks of time on a 1 GHz HP Alpha workstation.
External links
- GIMPS Discovers 40th Mersenne Prime (press release)