New explicit formulae for the prime counting function

Mladen Vassilev-Missana
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 1, Pages 44—49
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Authors and affiliations

Mladen Vassilev-Missana
5 V. Hugo Str., 1124 Sofia, Bulgaria

Abstract

In the paper new explicit formulae for the prime counting function π are proposed and proved. They depend on arbitrary positive arithmetic function which satisfies certain condition. As a particular case a formula for π depending on Euler’s function φ is obtained. To the author’s best knowledge such kind of formulae are proposed for the first time in the mathematical literature.

Keywords

  • Prime number
  • Composite number
  • Arithmetic function

AMS Classification

  • 11A25
  • 11A41

References

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  7. Vassilev-Missana, M. Three Formulae for n-th Prime and Six for n-th Term of Twin Primes, Notes on Number Theory and Discrete Mathematics, Vol. 7, 2001, No. 1, 15–20.
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Cite this paper

APA

Vassilev-Missana, M. (2013). New explicit formulae for the prime counting function, Notes on Number Theory and Discrete Mathematics, 19(1), 44-49.

Chicago

Vassilev-Missana, Mladen. “New Explicit Formulae for the Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19, no. 1 (2013): 44-49.

MLA

Vassilev-Missana, Mladen. “New Explicit Formulae for the Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19.1 (2013): 44-49. Print.

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