On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers

Authors: K rcaron í zcaron ek M.¹; Luca F.²; Somer L.³

Source: Journal of Number Theory, Volume 97, Number 1, November 2002 , pp. 95-112(18)

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Abstract:

We examine densities of several sets connected with the Fermat numbers F_m=2^2m+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).

Keywords: Fermat numbers; elite primes; sum of reciprocals; density.

Language: English

Document Type: Research article

DOI: http://dx.doi.org/10.1006/jnth.2002.2782

Affiliations: 1: Academy of Sciences, Z breve itná 25, Prague 1, CZ-115 67, Czech Republic itná 25, Prague 1, CZ-115 67, Czech Republic "> 2: Campus Morelia, Apartado Postal 61 - 3 (Xangari), Morelia, Michoacán, CP 58 089, Mexico 3: Department of Mathematics, Catholic University of America, Cardinal Station, Washington, District of Columbia, 20064