1. The problem statement, all variables and given/known data If p>=5 is prime, prove that p^2 +2 is composite. 2. Relevant equations If we took p and divided it by 6 we would get remainder possibilities of 0, 1, 2,3,4,5 3. The attempt at a solution p=6q p^2=36q^2 P^2=6(r) P^2+2=6r+2=2(3r+1) composite p=6q+1 p^2=36q^2+12q+1 = 12(r)+1 p^2+2=12r+3 = 3(4r+1) composite similarly 6q+2, 6q+4, 6q+5 But 6q+3 p^2= 36q^2+36q+9 = 9(4q^2)+4q+1) p^2=9r+2 ??????? How do I show this one is composite????