Question: prove 2^n-1 is not prime?
Answer: Since x-1 divides xn-1, for the latter to be prime the former must be one. ... Let a and n be integers greater than one. If an-1 is prime, then a is 2 and n is prime. Usually the first step in factoring numbers of the forms an-1 (where a and n are positive integers) is to factor the polynomial xn-1.