{
  "id": "2004.10273",
  "version": "v1",
  "published": "2020-04-21T20:10:06.000Z",
  "updated": "2020-04-21T20:10:06.000Z",
  "title": "Primes in numerical semigroups",
  "authors": [
    "Jorge L. Ramirez Alfonsin",
    "Mariusz Skalba"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-21T20:10:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D07",
      "11N13",
      "11A41"
    ],
    "keywords": [
      "numerical semigroup",
      "frobenius number",
      "prime number",
      "product ab"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}