SUR LA GÉNÉRATION D'UN NOMBRE INFINI DE NOMMETS PREMIERS JUMEAUX

In this work, we study the set of odd integers x > 1 such that x(x+2) is coprime with the product of the first n odd primes. We prove that the smallest such x is always a prime, and that it generates a twin prime pair (x, x+2) for infinitely many values of n . As a consequence, we provide a proof of the twin prime conjecture. Keywords: Twin primes, Odd integers, Prime number theory, Coprimality, Distribution of primes