suppose p and p square + 8 are prime. show that P cube +4 is also prime
Rewriting the question using LaTeX: Suppose $\displaystyle p$ and $\displaystyle p^2+8$ are prime, show that $\displaystyle p^3+4$ is also prime.
All primes $\displaystyle p$ other than 3 are of the form $\displaystyle 3k\pm 1$.
$\displaystyle p^2+8=(3k\pm 1)^2+8$
$\displaystyle =9k^2\pm 6k+9$, which is divisible by 3.
So, 3 is the only prime $\displaystyle p$ such that $\displaystyle p^2+8$ is also prime. Then, $\displaystyle p^3+4=31$ is also prime.