Let be two relatively prime integers and let be the numerical semigroup generated by and with Frobenius number . In this note, we prove that there exists a prime number with when the product is sufficiently large. Two related conjectures are posed and discussed as well.
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@article{CRMATH_2020__358_9-10_1001_0, author = {Ram{\'\i}rez Alfons{\'\i}n, J.L. and Ska{\l}ba, M.}, title = {Primes in numerical semigroups}, journal = {Comptes Rendus. Math\'ematique}, pages = {1001--1004}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {9-10}, year = {2020}, doi = {10.5802/crmath.104}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.104/} }
TY - JOUR AU - Ramírez Alfonsín, J.L. AU - Skałba, M. TI - Primes in numerical semigroups JO - Comptes Rendus. Mathématique PY - 2020 SP - 1001 EP - 1004 VL - 358 IS - 9-10 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.104/ DO - 10.5802/crmath.104 LA - en ID - CRMATH_2020__358_9-10_1001_0 ER -
%0 Journal Article %A Ramírez Alfonsín, J.L. %A Skałba, M. %T Primes in numerical semigroups %J Comptes Rendus. Mathématique %D 2020 %P 1001-1004 %V 358 %N 9-10 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.104/ %R 10.5802/crmath.104 %G en %F CRMATH_2020__358_9-10_1001_0
Ramírez Alfonsín, J.L.; Skałba, M. Primes in numerical semigroups. Comptes Rendus. Mathématique, Tome 358 (2020) no. 9-10, pp. 1001-1004. doi : 10.5802/crmath.104. http://www.numdam.org/articles/10.5802/crmath.104/
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