On the Sum of Reciprocals of Mersenne Primes

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2017Publisher:Scientific Research Publishing, Inc.Journal:American Journal of Computational Mathematics, volume 7, pages 145-148 (issn: 2161-1203, eissn: 2161-1211,

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Authors: Yoshihiro Tanaka;

doi: 10.4236/ajcm.2017.72012

On the Sum of Reciprocals of Mersenne Primes

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Abstract

The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where is the set of perfect powers of prime numbers.

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