# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# Mersenne primes

*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 โ 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}* = 2

*โ 1*

^{n}
i.e. a prime number that is one less than a power of two. For example, 31, which is 2^{5} โ 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.

**Show another (random) article**

Suggestions for corrections and ideas for articles are welcomed :

**Get in touch!**

Further resources :