A variant of the Euclid-Mullin sequence containing every prime
Andrew R. Booker
TL;DR
This paper generalizes Euclid's proof to create variants of the Euclid-Mullin sequence that are proven to include all prime numbers, expanding understanding of prime sequences.
Contribution
It introduces a new variant of the Euclid-Mullin sequence that is mathematically proven to contain every prime, a significant advancement over previous sequences.
Findings
The sequence contains all primes.
The generalization extends Euclid's proof.
Mathematically proven to include every prime.
Abstract
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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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Coding theory and cryptography · History and Theory of Mathematics