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In mathematics a Mersenne prime is a prime number of the form . They are named after the French monk Marin Mersenne who studied them in the early 17th century. The first four Mersenne primes are 3 7 31 and 127.If n is a composite number then so is 2n − 1. The definition is therefore unchanged when written where p is assumed prime.More generally numbers of the form without the primality requirement are called Mersenne numbers.