Prime $p$ with $p^2+8$ prime I need to prove that there is only one $p$ prime number such that $p^2+8$ is prime and find that prime.
Anyway, I just guessed and the answer is 3 but how do I prove that?

$p^2+8=0\pmod 3$ whenever $p=1,2\pmod 3$. For primes $p>3$, it is obvious that $p=1,2 \pmod 3$, and $p^2+8>3$, therefore $3$ is the only possible solution. 
