# Are Mersenne numbers with Mersenne prime exponent always prime?

A Mersenne number is a number on the form $$2^n-1$$. For it to be prime, the number $$n$$ must be prime. My question is that if $$n$$ is another Mersenne prime, will $$2^n-1$$ be always prime?

It seems so, to me anyway.

• If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48. – JavaMan Oct 15 '18 at 10:50

My own program found that $$2^{2^{13} - 1} - 1$$ is not a (probable) prime number, confirmed by Wolfram Alpha and https://oeis.org/A000043. Note that $$M_{13} = 8191$$ is prime and $$M_{8191}$$ is not.
• For me is says it is not (after a few seconds), query was isprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes. – gammatester Oct 15 '18 at 11:23