Mersenne prime

A prime number of the form \( M_p = 2^p-1 \) where \(p\) is prime.

... it is the greatest that will ever be discovered for, as they are merely curious without being useful, it is not likely that any person will attempt to find one beyond it.

-- Peter Barlow, 1811, on M31 = 2,147,483,647

Marin Mersenne

References and reviews

Factors of Mersenne Numbers

Not all the non-prime Mersennes have been completely factored. Some factoring data is

More of this factorisation data, including the known information for all exponents less than 200,000. Some other data taken from Robert Munafo's Large Number Notes page.