On the Sum of Reciprocals of Mersenne Primes - American Journal of Computational Mathematics

AJCM > Vol.7 No.2, June 2017

American Journal of Computational Mathematics

Volume 7, Issue 2 (June 2017)

ISSN Print: 2161-1203 ISSN Online: 2161-1211

Google-based Impact Factor: 0.42 Citations

On the Sum of Reciprocals of Mersenne Primes ()

HTML XML

Download as PDF (Size: 396KB) PP. 145-148

DOI: 10.4236/ajcm.2017.72012 1,708 Downloads 3,475 Views Citations

Author(s)

Yoshihiro Tanaka

Affiliation(s)

Faculty of Economics and Business, Hokkaido University, Sapporo, Japan.

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.

KEYWORDS

Mersenne Primes, the Sum of Reciprocals, Unresolved Problem

Share and Cite:

Tanaka, Y. (2017) On the Sum of Reciprocals of Mersenne Primes. American Journal of Computational Mathematics, 7, 145-148. doi: 10.4236/ajcm.2017.72012.

Cited by

[1]	Studies on the Valuations of Sequences
	2022

[2]	Combinatorial and Arithmetical Properties of Families of Sequences
	2021

[3]	Arithmetic properties of the sum of divisors
	2020

Journals Menu

Follow SCIRP

	+1 323-425-8868
	customer@scirp.org
	+86 18163351462(WhatsApp)
	1655362766

	Paper Publishing WeChat

Journals Menu

Home

About SCIRP

Service

Policies