Mersenne Primes are a specific case of Prime Numbersplugin-autotooltip__plain plugin-autotooltip_bigPrime Numbers

Since all other whole numbers (except 0) can be produced by multiplying together primes – they must be considered fundamental.

(1), 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 &etc

There are an infinite number of primes - as proved by Euclid around 300B.C. (first described by the French mathematician Martin Mersenne in the early 17th century.

They take the form of M_n = 2ⁿ − 1

i.e. a prime number that is one less than a power of two. For example, 31, which is 2⁵ − 1.

It's not currently known if there are an infinite number of Mersenne Primes. To date, only 51 have been discovered. The search is significantly driven by a distributed computing project known as the Great Internet Mersenne Prime Search.

It's also not known whether infinitely many Mersenne numbers with prime exponents are composite, i.e. they can be formed by multiplying two smaller positive integers.

There are no theorems for predicting the next Mersenne Primes, though there are conjectures about their distribution. See : PrimePages , University of Tennessee at Martin.