Prove that if $\displaystyle p > 3$ is prime then $\displaystyle p, p+2, p+4$ cannot all be prime.
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Anyone? I can certainly see why by just picking any prime, but can't prove it.
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.
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