Prime counting function π

Jan Górowski; Adam Łomnicki

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2013)

  • Volume: 5, page 71-76
  • ISSN: 2080-9751

Abstract

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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.

How to cite

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Jan Górowski, and Adam Łomnicki. "Prime counting function π." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 5 (2013): 71-76. <http://eudml.org/doc/296388>.

@article{JanGórowski2013,
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.},
author = {Jan Górowski, Adam Łomnicki},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {prime number; prime counting function; congruence},
language = {pol},
pages = {71-76},
title = {Prime counting function π},
url = {http://eudml.org/doc/296388},
volume = {5},
year = {2013},
}

TY - JOUR
AU - Jan Górowski
AU - Adam Łomnicki
TI - Prime counting function π
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2013
VL - 5
SP - 71
EP - 76
AB - 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.
LA - pol
KW - prime number; prime counting function; congruence
UR - http://eudml.org/doc/296388
ER -

References

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  1. Górowski, J., Łomnicki, A.: 2013, Around the Wilson’s theorem, Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia V, 51-56. 
  2. Kaddoura, J., Abdul-Nabi, S.: 2012, On formula to compute primes and the n th prime, Applied Math. Sciences 6(76), 3751-3757. 
  3. Lagarias, J. C., Miller, V. S., Odlyzko, A. M.: 1985, Computing π(x): the Meissel-Lehmer method, Math. Comp. 44(170), 537-560. 
  4. Oliveira e Silva, T.: 2006, Computing π(x): the combinatorial method, Revista do Detua 4(6), 759-768. 
  5. Ribenboim, P.: 1991, The little book of big primes, Springer Verlag, New York. 
  6. Sierpiński, W.: 1962, Co wiemy a czego nie wiemy o liczbach pierwszych, PZWS, Warszawa. 
  7. Willans, C. P.: 1964, On formulae for the n-th prime, Math. Gaz. 48, 413-415. 

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