On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Affiliation:	^a Mathematical Institute, Academy of Sciences, Z?itná 25, CZ-115 67, Prague 1, Czech Republicf1krizek@math.cas.czf1 ^b Instituto de Matemáticas UNAM, Campus Morelia, Apartado Postal 61 - 3 (Xangari), CP 58 089, Morelia, Michoacán, Mexicof2fluca@matmor.unam.mxf2 ^c Department of Mathematics, Catholic University of America, Cardinal Station, Washington, District of Columbia, 20064, f3somer@cua.eduf3

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.

Keywords:	Fermat numbers elite primes sum of reciprocals density.
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