So, Prime triplet: if p is prime, then p+2 and p+4 are also prime. Prove that 3,5,7 is the only prime triplet. I have figured out that p = 2k+1, k > 1 then p+2 = 2k + 3 and p + 4 = 2k+5. I figure there will be three cases to prove i.e. p (prime), p + 2 (prime), p + 4 (not prime) p (prime), p + 2 (not prime), p + 4 (prime) p (prime), p + 2 (not prime), p +4 (not prime) Not sure how to continue. The solution is in the book, but I just want a little hint in the right direction....and I hoped writing it out again would give me some hint. I am just starting with number theory and haven't done many proofs in my life so this feels a little tough.