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A Graph Theoretic Formula for the Number of Primes $π(n)$
Published 20 Mar 2020 in math.CO | (2003.09475v1)
Abstract: 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.
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