Squares, Cubes and Prime numbers Suppose $p$  and $p^2+2$ are prime numbers, prove that $p^3+2$ is also a prime number. Actually I do not know what is the relationship among square numbers, cube numbers and prime numbers

Hint: if $p \equiv \pm 1 \mod 3$, then what is $p^2 + 2 \mod 3$? How many primes $p$ are there such that $p^2 + 2$ is also prime?
