English

A Graph Theoretic Formula for the Number of Primes $\pi(n)$

Combinatorics 2020-03-24 v1

Abstract

Let PR[n][n] be the graph whose vertices are 2,3,,n2,3,\ldots,n with vertex vv adjacent to vertex ww if and only if gcd(v,w)>1\gcd(v,w)>1. It is shown that π(n)\pi(n), the the number of primes no more than nn, equals the Lov\'{a}sz number of this graph. This result suggests new avenues for graph-theoretic investigations of number-theoretic problems.

Keywords

Cite

@article{arxiv.2003.09475,
  title  = {A Graph Theoretic Formula for the Number of Primes $\pi(n)$},
  author = {R. Jacobs and C. E. Larson},
  journal= {arXiv preprint arXiv:2003.09475},
  year   = {2020}
}