For any prime p5 prove that p2 2 is composite?

Answer 1

for prime p>= 5

p = (6n+/-1)

p^2 + 2 = 36n^2+1 +/- 12n +2 = 36n^2+3 +/- 12n

divisible by 3 and p^2+2 >= 27 so 2nd factor >=9 so not a prime or composite