Determine all possible
primes p such that each of p8, p4, p+8 and p+12 are also primes.
p, p4 and p8 are mutually unequal mod 3 (same as p, p1, p+1) so at least one of these is a multiple of three. But if they're all primes, then the "multiple" of three must be 3 itself. p or p4 can't be three or p8 is negative, so p8=3 is the only solution, resulting in p=11.
As a check, if p=11, p4=7, p8=3, and p+12=23 and indeed all are prime. Knowing that p+12 is prime is irrelevent to finding the solution, although it might have eliminated the one possibility had the condition failed to hold.

Posted by Paul
on 20071227 21:05:57 