Mersenne prime

Mersenne prime, in number theory, a prime number of the form 2ⁿ − 1 where n is a natural number. These primes are a subset of the Mersenne numbers, M_n. The numbers are named for the French theologian and mathematician Marin Mersenne, who asserted in the preface of Cogitata Physica-Mathematica (1644) that, for n ≤ 257, M_n is a prime number only for 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257. His list, however, contained...