Mersenne numbers are integers of the form
Mn=2n-1 (many authors
require that the exponent n be a prime). They are
of interest because the Mersenne primes (prime Mersenne
numbers) are among the oldest and most studied of all
These numbers are named after the French monk Mersenne because he encouraged many mathematicians to study them and incorrectly conjectured that the Mersenne numbers were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, and 257; and all the other Mersennes with n < 257 were composite. See Mersenne's conjecture for more information on this influential guess.
Related pages (outside of this work)