Mersenne number

A Mersenne number is a number of the form 2n - 1.

The Mersenne numbers are:

3, 7, 15*, 31, 63*, 127...

* not a Mersenne prime

Some Mersenne numbers are frequently used in computing like the Mersenne primes 127 and 2147483647.

There are infinite Mersenne numbers as there are infinite natural numbers.

Mersenne primes
It was studied by Marin Mersenne in the early 1600s and named after him. Mersenne primes are of the form 2p - 1, where p is a prime number. If p is composite, 2p - 1 is composite.

As of February 2013, 48 Mersenne primes are discovered, the latest (257885161 - 1) being the largest found prime number.