Comptes Rendus
no. 9-10
Théorie des nombres
Primes in numerical semigroups
J.L. Ramírez Alfonsín1  ; M. Skałba2
1 UMI2924 - Jean- Christophe Yoccoz, CNRS-IMPA, Brazil and Univ. Montpellier, CNRS, Montpellier, France
2 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1001-1004.

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.

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DOI : 10.5802/crmath.104
Classification : 11D07, 11N13
J.L. Ramírez Alfonsín 1 ; M. Skałba 2

1 UMI2924 - Jean- Christophe Yoccoz, CNRS-IMPA, Brazil and Univ. Montpellier, CNRS, Montpellier, France
2 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Primes in numerical semigroups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1001--1004},
     publisher = {Acad\'emie des sciences, Paris},
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J.L. Ramírez Alfonsín; M. Skałba. Primes in numerical semigroups. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1001-1004. doi : 10.5802/crmath.104. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.104/

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