# Mersenne number

**Mersenne numbers**are integers of the form M

_{n}=2

^{n}-1 (many authors require that the exponent

*n*be a prime). They are of interest because the Mersenne primes (prime Mersenne numbers) are among the oldest and most studied of all primes!

These numbers are named after the French monk Mersenne
because he encouraged many mathematicians to study them
and incorrectly conjectured that the Mersenne numbers were
prime for *n* = 2, 3, 5, 7, 13, 17, 19, 31, 67,
and 257; and all the other Mersennes with *n* < 257
were composite. See Mersenne's conjecture for more
information on this influential guess.

**See Also:** MersenneDivisor, Mersennes, GeneralizedRepunit

**Related pages** (outside of this work)

- Mersenne primes (history, theorems, and records)
- Divisors of Mersenne numbers
- If M
_{n}is prime, so is*n*.

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