On the convergence of series of reciprocals of primes related to the fermat numbers

Abstract

We examine densities of several sets connected with the Fermat numbers Fm= 22m + 1. In particular, we prove that the series of reciprocals of all prime divisors of Fermat numbers is convergent. We also show that the series of reciprocals of elite primes is convergent. © 2002 Elsevier Science (USA).