Binary expansions of prime reciprocals

Brenda Navarro-Flores, José M. González-Barrios and Raúl Rueda
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 4, Pages 724–736
DOI: 10.7546/nntdm.2023.29.4.724-736
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Authors and affiliations

Brenda Navarro-Flores
Department of Probability and Statistics, IIMAS,
Universidad Nacional Autónoma de México, Mexico City, Mexico

José M. González-Barrios
Department of Probability and Statistics, IIMAS,
Universidad Nacional Autónoma de México, Mexico City, Mexico

Raúl Rueda
Department of Probability and Statistics, IIMAS,
Universidad Nacional Autónoma de México, Mexico City, Mexico

Abstract

Prime numbers have been always of great interest. In this work, we explore the prime numbers from a sieve other than the Eratosthenes sieve. Given a prime number p, we consider the binary expansion of \frac{1}{p} and, in particular, the size of the period of \frac{1}{p}. We show some results that relate the size of the period to properties of the prime numbers.

Keywords

  • Prime numbers
  • Order induced by binary expansions
  • New sieve

2020 Mathematics Subject Classification

  • 11A41
  • 11B83

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Manuscript history

  • Received: 10 November 2022
  • Revised: 27 July 2023
  • Accepted: 13 November 2023
  • Online First: 21 November 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Navarro-Flores, B., González-Barrios, J. M., & Rueda, R. (2023). Binary expansions of prime reciprocals. Notes on Number Theory and Discrete Mathematics, 29(4), 724-736, DOI: 10.7546/nntdm.2023.29.4.724-736.

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