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 primes!
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.
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