TL;DR
The paper introduces the Euclid-Mullin graph, a structure representing all Euclid's proofs of infinite primes, and explores its properties, showing it is not a tree through theoretical and numerical analysis.
Contribution
It is the first to define and analyze the Euclid-Mullin graph, revealing its complex structure and proving it is not a tree.
Findings
The Euclid-Mullin graph encodes all Euclid's proofs of infinite primes.
The graph has a complex structure and is not a tree.
Theoretical and numerical methods were used to analyze its properties.
Abstract
We introduce the Euclid-Mullin graph, which encodes all instances of Euclid's proof of the infinitude of primes. We investigate structural properties of the graph both theoretically and numerically; in particular, we prove that it is not a tree.
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