The Euclid-Mullin graph

Andrew R Booker; Sean Irvine

doi:10.1016/j.jnt.2016.01.013

The Euclid-Mullin graph

Andrew R Booker, Sean Irvine

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

317 Downloads (Pure)

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.

Original language	English
Pages (from-to)	30-57
Number of pages	28
Journal	Journal of Number Theory
Volume	165
Early online date	4 Mar 2016
DOIs	https://doi.org/10.1016/j.jnt.2016.01.013
Publication status	Published - Aug 2016

Keywords

Prime numbers
Euclid–Mullin sequence

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10.1016/j.jnt.2016.01.013

Full-text PDF (accepted author manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at http://www.sciencedirect.com/science/article/pii/S0022314X16000767. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 356 KBLicence: CC BY-NC-ND

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Detecting squarefree numbers
Booker, A. R. (Principal Investigator)
1/07/13 → 1/07/15
Project: Research
L-functions and modular forms
Keating, J. P. (Co-Principal Investigator) & Booker, A. R. (Principal Investigator)
1/06/13 → 30/09/19
Project: Research
Explicit number theory, automorphic forms and L-functions
Booker, A. R. (Principal Investigator)
1/10/09 → 1/04/15
Project: Research

Cite this

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abstract = "We introduce the Euclid–Mullin graph, which encodes all instances of Euclid{\textquoteright}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.",

keywords = "Prime numbers, Euclid–Mullin sequence",

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AB - 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.

KW - Prime numbers

KW - Euclid–Mullin sequence

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DO - 10.1016/j.jnt.2016.01.013

M3 - Article (Academic Journal)

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VL - 165

SP - 30

EP - 57

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

The Euclid-Mullin graph

Abstract

Keywords

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Projects

Detecting squarefree numbers

L-functions and modular forms

Explicit number theory, automorphic forms and L-functions

Cite this