# primes

• October 20th 2011, 03:07 AM
claudio411
primes
suppose p and p square + 8 are prime. show that P cube +4 is also prime
• October 20th 2011, 09:27 AM
alexmahone
Re: primes
Quote:

Originally Posted by claudio411
suppose p and p square + 8 are prime. show that P cube +4 is also prime

Rewriting the question using LaTeX: Suppose $p$ and $p^2+8$ are prime, show that $p^3+4$ is also prime.

All primes $p$ other than 3 are of the form $3k\pm 1$.

$p^2+8=(3k\pm 1)^2+8$

$=9k^2\pm 6k+9$, which is divisible by 3.

So, 3 is the only prime $p$ such that $p^2+8$ is also prime. Then, $p^3+4=31$ is also prime.