Primes in numerical semigroups

Published 21 Apr 2020 in math.NT and math.CO | (2004.10273v1)

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.

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