## The Euclid-Mullin graph

*Booker, Andrew R.*;

*Irvine, Sean A.*;

- Journal: volume 165,pages30-57issn: 0022-314X
Related identifiers: - Subject: Prime numbers | Euclid–Mullin sequence | Mathematics - Number Theoryarxiv: Mathematics::History and Overview | Mathematics::General Mathematics | Astrophysics::Cosmology and Extragalactic Astrophysics | Astrophysics::Instrumentation and Methods for Astrophysics

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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