Numbers of the form M n = 2 n − 1 without the primality requirement may be called Mersenne numbers.
The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form M p = 2 p − 1 for some prime p. If n is a composite number then so is 2 n − 1. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.
That is, it is a prime number of the form M n = 2 n − 1 for some integer n.
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. Mersenne primes (of form 2^ p − 1 where p is a prime).
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