Some formulae which match with the prime counting function infinitely often

Yannick Saouter
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 1, Pages 1—4
DOI: 10.7546/nntdm.2018.24.1.1-4
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Authors and affiliations

Yannick Saouter
Lab-STICC Institut Mines Telecom Atlantique
655 Avenue du Technopole, 29200 Plouzane, France

Abstract

Recently K. Gaitanas gave a formula which matches with the counting prime function for an infinite set of values of its argument. In this note, we give a construction of an infinite number of such formulae.

Keywords

  • Prime numbers

2010 Mathematics Subject Classification

  • 11A41
  • 11A25
  • 11B75

References

  1. Gaitanas, K. (2015) An explicit formula for the prime counting function which is valid infinitely often. American Mathematical Monthly, 122, 3, 283.
  2. Golomb, S. W. (1962) On the ratio of n to π(n). American Mathematical Monthly, 69, 1, 36–37.
  3. Rosser, J. B., & Schoenfeld, L. (1962) Approximate formulas for some functions of prime numbers. Illinois Journal of Mathematics, 6, 1, 64–94.

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Cite this paper

APA

Saouter, Y. (2018). Some formulae which match with the prime counting function infinitely often. Notes on Number Theory and Discrete Mathematics, 24(1), 1-4, doi: 10.7546/nntdm.2018.24.1.1-4.

Chicago

Saouter, Yannick. “Some Formulae Which Match with the Prime Counting Function Infinitely Often.” Notes on Number Theory and Discrete Mathematics 24, no. 1 (2018): 1-4, doi: 10.7546/nntdm.2018.24.1.1-4.

MLA

Saouter, Yannick. “Some Formulae Which Match with the Prime Counting Function Infinitely Often.” Notes on Number Theory and Discrete Mathematics 24.1 (2018): 1-4. Print, doi: 10.7546/nntdm.2018.24.1.1-4.

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