Obviously, if p is prime, larger than or equal to 29, then both p+1, and p- 1 are even so it remains to show that one of the factors is divisible 7 and one by 13.
By Fermat’s little theorem, 13 divides . Also by Fermat’s little theorem, 7 divides and hence 7 divides . And obviously 2 divides since is odd. The result follows.
NB: This works for all integers which are coprime with 2, 7, and 13.