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, 282,589,933 − 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 NumberPMersenne Number (M)Prime?