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

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arxiv 1410.7008 v2 pith:NFJ3WONW submitted 2014-10-26 math.NT cs.NAmath.NA

Jan Büthe This is my paper · ORCID
classification math.NTcs.NAmath.NA
keywords methodanalyticcalculatingimprovedcalculatedcooperationexceedingfranke
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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 $\pi(10^{25})$.

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