Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Mersenne Prime Numbers

Mersenne prime numbers are numbers of the form

For m to be prime, p itself must be prime, but that is not sufficient. Indeed, at present only 43 Mersenne prime numbers are known. They are obtained by letting

p = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457.

Note that for example

so that for p = 11 we do not obtain a prime number.

The largest prime number known is a Mersenne prime number.

Mersenne prime numbers have their own web site which is dedicated to a netwide search for Mersenne prime numbers and related tasks.

Fine print, your comments, more links, Peter Alfeld, PA1UM

[06-Aug-1999]