Mersenne Primes

Certain prime numbers that follow $2^n-1$.

Proof

Assume $n$ is Composite Number Integers. $a,b\in Z,a<n,b<n$ $n=ab$ let $x=2^b-1$ let $y=1+2^b+2^{2b}+\dots 2^{(a-1)(b)}$ $xy=(2^b-1)(1+2^b+2^{2b}+2^{(a-1)(b)})$ $=(2^b+2^{2b}+\cdots +2^{ab})-(1+2^b+2^{2b}\cdots +2^{(a-1)(b)}$ $=2^{ab}-1=2^n-1$