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arXiv · 2002.12797

An algorithm for the prime-counting function of primes larger than three

Yuri Heymann
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Abstract

The prime-counting function $\pi(x)$ which computes the number of primes smaller or equal to a given real number has a long-standing interest in number theory. The present manuscript proposes a method to compute $\pi(x)$ with time complexity $\mathcal{O}(x^{1/2})$ without the need to introduce the non-trivial zeros of the Riemann zeta function.

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Yuri Heymann. 2020-02-28. An algorithm for the prime-counting function of primes larger than three. https://arxiv.org/abs/2002.12797

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