English

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

General Mathematics 2020-03-24 v3

Abstract

The prime-counting function π(x)\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 π(x)\pi(x) with time complexity O(x1/2)\mathcal{O}(x^{1/2}) without the need to introduce the non-trivial zeros of the Riemann zeta function.

Keywords

Cite

@article{arxiv.2002.12797,
  title  = {An algorithm for the prime-counting function of primes larger than three},
  author = {Yuri Heymann},
  journal= {arXiv preprint arXiv:2002.12797},
  year   = {2020}
}

Comments

Issue with double counting of composites

R2 v1 2026-06-23T13:57:49.411Z