A prime pair consists of two primes that differ by two. There are many prime pairs, for example, 11 and 13, 17 and 19, etc. Prime triplets are three numbers n 2, n + 2, n + 4 that are all prime. Show that the only prime triplet is (3,5,7). Prove by contradiction.

Hint: The idea is to reach to a contradiction. The basis of the test is to assume that there is a triplet of primes (n, n+2, n+4) different from (3,5,7). If you prove that n, n+2 or n+4 are not primes or that n, n+2, n+4 are precisely 3, 5 and 7, the demonstration is ready. You have to find the common divisors that n, n+2 and n+4 have and manipulate them algebraically to solve the problem.