Determine all possible
primes p such that each of p8, p4, p+8 and p+12 are also primes.
(In reply to
computer exploration (spoiler) by Charlie)
By inspection, p=2 and p=3 aren't solutions.
All other primes can be expressed in one of 2 forms, either 6k+1 or 6k1.
For p=6k+1, p4=6k3, which can only be prime if k=1.
But then p8=6k7= 1 which is impossible.
So p=6k1 and p8=6k9 which is prime only for k=2 and p=11, whence p4=7, p+8=19, and p+12=23.

Posted by xdog
on 20071226 12:28:44 