Primes in numerical semigroups

2020/04/21 by Alfonsin, Jorge L. Ramirez, Skalba, Mariusz · 2 citations
#11A41 #11D07 #11N13 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.10273

Abstract

Let 0 < a < b be two relatively prime integers and let 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 with p < g(a,b) when the product ab is sufficiently large. Two related conjectures are posed and discussed as well.

Cited by

• Primes of the form ax+by
• The number of primes not in a numerical semigroup

Related

• The Frobenius problem for generalized repunit numerical semigroups
• A Note on Generalized Repunit Numerical Semigroups
• On quotients of numerical semigroups for almost arithmetic progressions
• On the Frobenius Number of Quotients of Numerical Semigroups
• On the Frobenius Number and Genus of a Collection of Semigroups Generalizing Repunit Numerical Semigroups