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A practical analytic method for calculating $ \pi(x)$


Authors: Jens Franke, Thorsten Kleinjung, Jan Büthe and Alexander Jost
Journal: Math. Comp. 86 (2017), 2889-2909
MSC (2010): Primary 11Y35; Secondary 11Y70
DOI: https://doi.org/10.1090/mcom/3038
Published electronically: March 30, 2017
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Abstract: In this paper we give a description of a practical analytic method for the computation of $ \pi (x)$, the number of prime numbers $ \leq x$. The method is similar to the one proposed by Lagarias and Odlyzko but uses the Weil-Barner explicit formula instead of curve integrals.


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Additional Information

Jens Franke
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Thorsten Kleinjung
Affiliation: Laboratory for Cryptologic Algorithms, EPFL, Station 14, CH-1015 Lausanne, Switzerland

Jan Büthe
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Alexander Jost
Affiliation: Graurheindorfer Strasse 64, 53111 Bonn, Germany

DOI: https://doi.org/10.1090/mcom/3038
Received by editor(s): October 7, 2013
Received by editor(s) in revised form: November 11, 2014
Published electronically: March 30, 2017
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society