About the theorem that partially solves the Navarrete–Orellana Conjecture

Jorge Andrés Julca Avila and Gabriel Silva de Andrade
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 302–317
DOI: 10.7546/nntdm.2022.28.2.302-317
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Authors and affiliations

Jorge Andrés Julca Avila
Department of Mathematics and Statistics, Federal University of São João del-Rei (UFSJ),
São João del-Rei, 36307-352/MG, Brazil

Gabriel Silva de Andrade
Professional Master Degree Program in Mathematics in National Network – PROFMAT,
CSA/UFSJ, São João del-Rei, 36307-352/MG, Brazil


The Navarrete–Orellana Conjecture states that “given a large prime number a sequence is generated, in such a way that all odd prime numbers, except the given prime, are fixed points of that sequence”. In this work, we formulated a theorem that partially confirms the veracity of this conjecture, more specifically, all prime numbers of a given line segment are fixed points of this sequence.


  • Prime numbers
  • Triangular numbers
  • Fixed points
  • Sequence family
  • Conjecture

2020 Mathematics Subject Classification

  • 11A41
  • 11B83
  • 11Y55


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Manuscript history

  • Received: 5 June 2021
  • Revised: 13 May 2022
  • Accepted: 7 June 2022
  • Online First: 10 June 2022

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Cite this paper

Avila, J. A. J., & De Andrade, G. S. (2022). About the theorem that partially solves the Navarrete–Orellana Conjecture. Notes on Number Theory and Discrete Mathematics, 28(2), 302-317, DOI: 10.7546/nntdm.2022.28.2.302-317.

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