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Mersenne Numbers

A 'Mersenne Prime' is prime number one less than a power of two. That is, a prime number of the form M = 2ⁿ - 1 for some integer n. They're named after Marin Mersenne (1588-1648), a French friar, who studied them in the early 19th century. If n is composite (not prime), then M is also composite. If n is prime, M may or may not be prime.

The smallest composite Mersenne number with a prime exponent p is 2¹¹ − 1 = 2047 = 23 × 89.

The largest known prime number, 2^82,589,933 − 1, is a Mersenne prime.

See "Mersenne Prime" in Wikipedia.

Also see the "Online Encyclopedia of Integer Sequences: Mersenne Primes here.

The Mersenne Numbers Less than 10,000 for Prime P

Nth Number	P	Mersenne Number (M)	Prime?
1	2	3	Prime
2	3	7	Prime
3	5	31	Prime
4	7	127	Prime
5	11	2,047	Prime
6	13	8,191	Prime

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