New consequences of prime-counting function

Sadani Idir
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 25–31
DOI: 10.7546/nntdm.2021.27.4.25-31
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Sadani Idir

Department of Mathematics, University of Mouloud Mammeri
15000 Tizi-Ouzou, Algeria

Abstract

Our objective in this paper is to study a particular set of prime numbers, namely \left\{p\in\mathbb{P} \ \text{and} \ \pi(p)\notin\mathbb{P}\right\}\!. As a consequence, estimations of the form \sum{f(p)} with p
being prime belonging to this set are derived.

Keywords

  • Prime number
  • Prime-counting function
  • Partition

2020 Mathematics Subject Classification

  • 11A41

References

  1. Hadamard, J. (1896). Sur la distribution des zeros de la fonction ζ(s) et ses consequences arithmetiques, Bulletin de la Societe Mathematique de France, 24, 199–220.
  2. de la Vallee Poussin, C.-J. (1896). Recherches analytiques sur la theorie des nombres premiers, Annales de la Societe scientifique de Bruxelles, 20, 183–256.
  3. de la Vallee Poussin, C.-J. (1899). Sur la fonction ζ(s) de Riemann et le nombre des nombres premiers inferieurs a une limite donnee, Memoires couronnes et autres Memoires in-8 publies par l’Academie royale de Belgique, 59, 1–74.
  4. Idir, S. (2017). Study of Some Equivalence Classes of Primes. Notes on Number Theory and Discrete Mathematics, 23(2), 21–29.

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Cite this paper

Idir, S. (2021). New consequences of prime-counting function. Notes on Number Theory and Discrete Mathematics, 27(4), 25-31, DOI: 10.7546/nntdm.2021.27.4.25-31.

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