Improving the estimates for a sequence involving prime numbers

Christian Axler
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 8—13
DOI: 10.7546/nntdm.2019.25.1.8-13
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Authors and affiliations

Christian Axler
Department of Mathematics, University of Düsseldorf
40225 Düsseldorf, Germany

Abstract

Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence Cn = npn − ∑k ≤ n pk, n ≥ 1, involving the prime numbers.

Keywords

  • Prime counting function
  • Prime numbers
  • Sum of primes

2010 Mathematics Subject Classification

  • 11N05
  • 11A41

References

  1. Axler, C. (2015). On a sequence involving prime numbers, J. Integer Seq., 18, no. 7, Article 15.7.6, 13 pp.
  2. Axler, C. (2018). New estimates for some functions defined over primes, Integers, 18, Paper No. A52, 21 pp. 12
  3. Gauß, C. F. (1876). Werke, 2 ed., Königlichen Gesellschaft der Wissenschaften, Göttingen.
  4. Hadamard, J. (1896). Sur la distribution des zéros de la fonction (s) et ses conséquences arithmétiques, Bull. Soc. Math. France, 24, 199–220.
  5. de la Vallée Poussin, C.-J. (1896). Recherches analytiques la théorie des nombres premiers, Ann. Soc. scient. Bruxelles, 20, 183–256.
  6. de la Vallée Poussin, C.-J. (1899). Sur la fonction (s) de Riemann et le nombre des nombres premiers inférieurs à une limite donnée, Mem. Couronn´es de l’Acad. Roy. Sci. Bruxelles, 59, 1–74.

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Cite this paper

APA

Axler, C. (2019). Improving the estimates for a sequence involving prime numbers. Notes on Number Theory and Discrete Mathematics, 25(1), 8-13, doi: 10.7546/nntdm.2019.25.1.8-13.

Chicago

Axler, Christian. “Improving the Estimates for a Sequence Involving Prime Numbers.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 8-13, doi: 10.7546/nntdm.2019.25.1.8-13.

MLA

Axler, Christian. “Improving the Estimates for a Sequence Involving Prime Numbers.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 8-13. Print, doi: 10.7546/nntdm.2019.25.1.8-13.

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