We use the factor theorem, which is the identity: 
(+ ··· +  + ··· + )
Suppose p is divisible by 4, then there exists 
positive integer q such that p=4q, then 
 =
(+ ··· +  + ··· + ) =
15(+ ··· +  + ··· + ) so 
 is either 15 (when q=1) or divisible 
by 15, and in either case is not prime.

For the case when p is divisible by 3, then there exists 
positive integer q such that p=3q. Do the same as
above and you have 7 where the 15 is above and 
is not prime unless it equals 7, i.e., unless q=1, i.e.,
unless p=3, but that is ruled out in the hypothesis.
Edwin