An improved analytic Method for calculating $π(x)$
arXiv:1410.70088 citationsh-index: 2
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Provides a new benchmark value for the prime counting function, relevant to number theory researchers.
The authors improved an analytic method for computing π(x) and used it to calculate π(10^25).
We present an improved version of the analytic method for calculating $π(x)$, 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 $π(10^{25})$.