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]