1. ## mersenne primes

I understand how you find these primes but how do you prove it? It seems so simple because you can just plug in numbers but thats not a mathematical proof.

Prove that if (2^n)-1 is prime, then n is prime.

2. Originally Posted by hero
I understand how you find these primes but how do you prove it? It seems so simple because you can just plug in numbers but thats not a mathematical proof.

Prove that if (2^n)-1 is prime, then n is prime.
Simple. Use my hint below.

Hint1: If n>1 is not prime then n=a*b where 1<a,b

Hint2: Use the identity, (x^n-y^n)=(x-y)(x^{n-1}+x^{n-2}y+...+y^{n-1})