Prove that 11 is the only prime of the form p^2 + 2, with p prime

Proof:

  Let n = p^2 + 2
  If n is 11, p is 3
  If n is not 11, p must be either of the form 3a+1 or 3a+2, with a ∈ ℕ

  Suppose p = 3a+1
  n = p^2 + 2 = (3a+1)^2 + 2 = 9a2 + 6a + 3

  Suppose p = 3a+2
  n = p^2 + 2 = (3a+2)^2 + 2 = 9a2 + 12a + 6

  In both cases, n is divisible by 3 and therefore not prime
  Thus 11 is the only prime of the form p^2+2, with p prime

# posted by rot13(Unafba Pune) @ 12:47 PM