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A Graph Theoretic Formula for the Number of Primes $\pi(n)$ by Jacobs, R.; Larson, C. E. is a scholarly article available to read on EtoBox.

What is A Graph Theoretic Formula for the Number of Primes $\pi(n)$ about?

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

Author

Jacobs, R.; Larson, C. E.

Published

2020

Language

EN