text: Well, p can take only 6k+1 or 6k+5 because\n\n6k is divisible by 6\n6k+1 OK\n6k+2 is divisible by 2\n6k+3 is divisible by 3\n6k+4 is divisible by 2\n6k+5 OK\n\nAnd then after that it goes back to 6k.\n\nCASE 1 : p = (6k+1)^2 + 2 = 36k^2+12k+3\nCan be factored into 3(12k^2+4k+1), therefore divisible by 3, and not prime\n\nCASE 2 : p = (6k+5)^2 + 2 = 36k^2 + 60k + 27\n\nAlso divisible by 3 for the same reason as Case 1.