# Math Help - Prime Proof

1. ## Prime Proof

Prove that if $p > 3$ is prime then $p, p+2, p+4$ cannot all be prime.

2. Anyone? I can certainly see why by just picking any prime, but can't prove it.

3. If p is prime you know p mod 3 = 1 or 2, if p mod 3 = 1 you have (p + 2) mod 3 = 0, so p+2 is divisible by 3 and if p mod 3 = 2 you have (p + 4) mod 3 = 0, so that p+4 is divisible by three.