回复：Mersenne primes

1) proof of 4^x-1 is divisible by 3.
a_1=4^1-1=3 is divisible by 3
let a_x is divisible by 3. then we have a_(x+1)=4*4^x-1
=4(4^x-1)+3. so a_(x+1) is divisible by 3.
and prove: 4^x-1 is divisible by 3.

2) when n=2x, 2^n-1=4^x-1. then 2^n-1 is divisible by 3. controdiction to conditions (2^n-1 is a prime).

3) when n=2x+1, 2^n-1=2*4^x-1. 2^n+1=2*4^x+1=2*(4^x-1)+3 and is divisible by 3. Thus 2^n+1 is not a prime.