Introduction to Twin Primes and Brun's Constant 1 Introduction It's a very old fact (Euclid 325-265 B.C., in Book IX of the Elements) that the set of primes is infinite and a much more recent and famous result (by Jacques Hadamard (1865-1963) and Charles-Jean de la Vallee Poussin (1866-1962)) that the density of primes is ruled by the law p(n) ~ n log(n) where the prime counting function p(n) is ...