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
Full paper (PDF, 159 Kb)

Details

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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