Résumé
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 ∈ 〈a, b〉 with p < g (a, b) when the product ab is sufficiently large. Two related conjectures are posed and discussed as well.