M40

M40 is the short hand used to refer to the 40th Mersenne prime. Specifically it is $2^{20996011}-1$. 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)