Sequences of Prime Reciprocals. Preliminaries

Author:

Grabowski Adam1

Affiliation:

1. Institute of Informatics , University of Białystok , Poland

Abstract

Summary In the article we formalize some properties needed to prove that sequences of prime reciprocals are divergent. The aim is to show that the series exhibits log-log growth. We introduce some auxiliary notions as harmonic numbers, telescoping series, and prove some standard properties of logarithms and exponents absent in the Mizar Mathematical Library. At the end we proceed with square-free and square-containing parts of a natural number and reciprocals of corresponding products.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Reference11 articles.

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5. [5] Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.10.1007/978-3-642-14128-7_26

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1. The Divergence of the Sum of Prime Reciprocals;Formalized Mathematics;2022-10-01

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