An improved analytic Method for calculating $\pi(x)$

Jan Büthe

An improved analytic Method for calculating $\pi(x)$

Number Theory 2015-11-09 v2 Numerical Analysis

Authors: Jan Büthe

Abstract

We present an improved version of the analytic method for calculating $\pi(x)$ , the number of prime numbers not exceeding $x$ . We implemented this method in cooperation with J. Franke, T. Kleinjung and A. Jost and calculated the value $\pi(10^{25})$ .

Keywords

pi computation prime numbers

Cite

@article{arxiv.1410.7008,
  title  = {An improved analytic Method for calculating $\pi(x)$},
  author = {Jan Büthe},
  journal= {arXiv preprint arXiv:1410.7008},
  year   = {2015}
}

Comments

21 pages, v2 is a rewrite of v1, title changed from 'A practical analytic method for calculating $\pi(x)$ II' to 'An improved analytic Method for calculating $\pi(x)$

Related papers

View all related →