Primes in numerical semigroups
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.
math.NT↗