[jcoffland]

tl;dr The 50th Mersenne prime was just found by a volunteer of the GIMPS (Great Internet Mersenne Prime Search) project. It is 2^77,232,917-1 and has 23,249,425 digits. Mersenne primes are extremely rare and are always of the form 2^p-1 for some positive integer p. The first four Mersenne primes are 3, 7, 31, and 127.

[meta_AU]

Also, p is prime.

[dansunciel]

Just to clarify, in this case p = 77,232,917 is prime, but for Mersenne primes in general p is just a positive integer.

[meta_AU]

Not quite. If p isn't prime then 2^p - 1 isn't prime.