Prove that $8p^2+2p+1$ is prime number

Question

If $p$ and $8p^2+1$ is prime number than $$8p^2+2p+1$$ is prime number proof.

I know that prime number can write as a multiply 1 and $8p^2+2p+1$, so if I show that this number is a multiply $a*b$ where $a\not=1$ and $b\not=1$ than that is not a prime number, can someone help me?

Answer 1

If $p = 3k\pm 1$ then $8p^2+1 \equiv 0 \pmod3$ so $8p^2+1=3$ which is imposibile. So $p=3$ then $8p^2+2p+1 = 79$