Mersenne Primes

Mersenne Primes take the form $p = 2^k - 1$. Often we just loop through all possible Mersenne primes and check if either $p$ or $q$ are that.

This is very easy to do in Sage:

from sage.combinat.sloane_functions import A000668

mersenne = A000668()

Then we can grab the $n$th Mersenne prime using mersenne(n).