If a product of three or more three prime numbers then each one must be . Because otherwise we get that .

If where the factors are non-trivial then . Which cannot be prime.Let p>1, if (2^p) - 1 is prime, prove that p is prime. [Hint: Prove the contrapositive: If p is composite, so is (2^p) - 1. Note: The convers is false]

Factorize,let a, b be nonnegative integers not both 1. If k is odd and k >= (greater than or equal) 3, prove that a^k + b^k is not prime.

If each prime factor was of the form 4k+1 then n would too.if n is a positive integer of the form 4k +3, prove that n has a prime factor of the form 4k + 3.