Are all prime numbers greater than 2 odd?

prime-numbers

#1

Are all prime numbers greater than 2 odd?

Answer:

Yes. Proof: Let q be a prime number greater than 2 such that q is even. By definition of evenness, that means there exists an integer k such that q=2k. Hence 2 is a factor of q. As a prime number only has a single factor of itself and 1, this means that q must be 2. But we said that q > 2. Contradiction. Hence there must be no such thing as an even prime number greater than 2.