Prime counting function π

Authors

  • Jan Górowski Instytut Matematyki, Uniwersytet Pedagogiczny w Krakowie
  • Adam Łomnicki Instytut Matematyki, Uniwersytet Pedagogiczny w Krakowie

Keywords:

prime number, prime counting function, congruence

Abstract

The aim of this paper is to derive new explicit formulas for thefunction π, where π(x) denotes the number of primes not exceeding x. Some justifications and generalisations of the formulas obtained by Willans (1964),Minac (1991) and Kaddoura and Abdul-Nabi (2012) are also obtained.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

Górowski, J., Łomnicki, A.: 2013, Around the Wilson’s theorem, Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia V, 51-56.

Kaddoura, J., Abdul-Nabi, S.: 2012, On formula to compute primes and the n th prime, Applied Math. Sciences 6(76), 3751-3757.

Lagarias, J. C., Miller, V. S., Odlyzko, A. M.: 1985, Computing π(x): the Meissel-Lehmer method, Math. Comp. 44(170), 537-560.

Oliveira e Silva, T.: 2006, Computing π(x): the combinatorial method, Revista do Detua 4(6), 759-768.

Ribenboim, P.: 1991, The little book of big primes, Springer Verlag, New York.

Sierpiński, W.: 1962, Co wiemy a czego nie wiemy o liczbach pierwszych, PZWS, Warszawa.

Willans, C. P.: 1964, On formulae for the n-th prime, Math. Gaz. 48, 413-415.

Downloads

Published

2017-07-05

How to Cite

Górowski, J., & Łomnicki, A. (2017). Prime counting function π. Annales Universitatis Paedagogicae Cracoviensis | Studia Ad Didacticam Mathematicae Pertinentia, 5, 71–76. Retrieved from https://didacticammath.uken.krakow.pl/article/view/3671

Issue

Vol. 5 (2013)

Section

Contents

License

Read the full statement of the license to publish PDF file.

(see English version) (see Polish version)