Determine all possible primes p such that each of p-8, p-4, p+8 and p+12 are also primes.

All primes greater than 3 are of 6k+1 or 6k-1
Let p-8 > 11 => p>19

Case(i): Let p=6k-1
then p-8 = 6k-9 = 3*(2k-3)
So, p-8 is not prime

Case(ii): Let p=6k+1
then p-4 = 6k-3 = 3*(2k-1)
So, p-4 is not prime in this case
p<19
The only value that satisfies these conditions is p=11.

Posted by Praneeth on 2007-12-27 00:49:41