{
  "id": "0910.2960",
  "version": "v3",
  "published": "2009-10-15T18:36:40.000Z",
  "updated": "2011-03-02T01:18:58.000Z",
  "title": "Jumping champions and gaps between consecutive primes",
  "authors": [
    "D. A. Goldston",
    "A. H. Ledoan"
  ],
  "comment": "7 pages, 1 table",
  "categories": [
    "math.NT"
  ],
  "abstract": "The most common difference that occurs among the consecutive primes less than or equal to $x$ is called a jumping champion. Occasionally there are ties. Therefore there can be more than one jumping champion for a given $x$. In 1999 A. Odlyzko, M. Rubinstein, and M. Wolf provided heuristic and empirical evidence in support of the conjecture that the numbers greater than 1 that are jumping champions are 4 and the primorials 2, 6, 30, 210, 2310,... As a step towards proving this conjecture they introduced a second weaker conjecture that any fixed prime $p$ divides all sufficiently large jumping champions. In this paper we extend a method of P. Erd\\H{o}s and E. G. Straus from 1980 to prove that the second conjecture follows directly from the prime pair conjecture of G. H. Hardy and J. E. Littlewood.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-02T01:18:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11P32",
      "11N36"
    ],
    "keywords": [
      "consecutive primes",
      "second weaker conjecture",
      "prime pair conjecture",
      "numbers greater",
      "common difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2960G"
    }
  }
}