2011/024) if p and p^2 + 8 are both primes then prove p^3+4 is a prime

proof:
p is either 2 or 3 or of the form (6n+/-1)

if p is of the form (6n+/-1)

then p^2 + 8 = 36n^2-12n + 9 = 3 ( 12n^2 - 4n + 3) divisible by 3 and ( 12n^2 - 4n + 3) > 1

so not a prime

if p = 2 then p^2 + 8 is even and not a prime

so only p =3 is left and p^2+ 8 = 17 is a prime and p =3 is the only number satisfies the criteria and p^3+ 4 = 31 is a prime as well