Prove that there are infinitely many primes of the form 4n + 3; of the form 6n + 5. (h) remark the last problem can be stated thus: each of the arithmetic progressions 3,7,11,15, 19, infinitude of primes. one of the famous theorems of number theory (the proof of which lies deeper than the methods of this book), due to dirichlet, is that the arithmetic progression a, a + b, a + 2b, a + 3b, are relatively prime, that is if (a, b) = 1. and 5, 11, 17, 23,29, contains an contains infinitely many primes if the integers a and b > 0