Journal of Integer Sequences, Vol. 19 (2016), Article 16.6.4

A Variant of the Euclid-Mullin Sequence Containing Every Prime

Andrew R. Booker
Howard House
University of Bristol
Queens Avenue
Bristol, BS8 1SN
United Kingdom


We consider a generalization of Euclid's proof of the infinitude of primes and show that it leads to variants of the Euclid-Mullin sequence that provably contain every prime number.

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(Concerned with sequences A000945 A000946 A167604.)

Received May 26 2016; revised versions received June 16 2016; June 17 2016. Published in Journal of Integer Sequences, July 4 2016.

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