Primes in numerical semigroups
Number Theory
2020-04-23 v1 Combinatorics
Abstract
Let 0 < a < b be two relatively prime integers and let <a,b> be the numerical semigroup generated by a and b with Frobenius number g(a,b)=ab-a-b. In this note, we prove that there exists a prime number p in <a,b> with p < g(a,b) when the product ab is sufficiently large. Two related conjectures are posed and discussed as well.
Cite
@article{arxiv.2004.10273,
title = {Primes in numerical semigroups},
author = {Jorge L. Ramirez Alfonsin and Mariusz Skalba},
journal= {arXiv preprint arXiv:2004.10273},
year = {2020}
}