you will need to prove that if n is not prime then 2^n - 1 is prime as well. So basically you just need to let n=pq, and then just let 2^n - 1 = 2^pq - 1, then you can factorise it into (2^p - 1) (2^p(q-1) + 2^p(q-2) + ... + 1) which proves the thing pretty much instantly.
you will need to prove that if n is not prime then 2^n - 1 is prime as well. So basically you just need to let n=pq, and then just let 2^n - 1 = 2^pq - 1, then you can factorise it into (2^p - 1) (2^p(q-1) + 2^p(q-2) + ... + 1) which proves the thing pretty much instantly.