{
  "id": "1506.03359",
  "version": "v1",
  "published": "2015-06-10T15:25:12.000Z",
  "updated": "2015-06-10T15:25:12.000Z",
  "title": "An asymptotic upper bound on prime gaps",
  "authors": [
    "André LeClair"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The Cram\\'er-Granville conjecture is an upper bound on prime gaps, $p_{n+1} - p_n < c \\, \\log^2 p_n$ for some constant $c\\geq 1$. Using a formula of Selberg, we demonstrate the validity of the conjecture in the limit of large $n$ with $c=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-10T15:25:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic upper bound",
      "prime gaps",
      "cramer-granville conjecture",
      "demonstrate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150603359L"
    }
  }
}