{
  "id": "1412.5029",
  "version": "v1",
  "published": "2014-12-16T14:57:45.000Z",
  "updated": "2014-12-16T14:57:45.000Z",
  "title": "Long gaps between primes",
  "authors": [
    "Kevin Ford",
    "Ben Green",
    "Sergei Konyagin",
    "James Maynard",
    "Terence Tao"
  ],
  "comment": "39 Pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p_n$ denotes the $n$-th prime. We prove that $$\\max_{p_{n+1} \\leq X} (p_{n+1}-p_n) \\gg \\frac{\\log X \\log \\log X\\log\\log\\log\\log X}{\\log \\log \\log X}$$ for sufficiently large $X$, improving upon recent bounds of the first three and fifth authors and of the fourth author. Our main new ingredient is a generalization of a hypergraph covering theorem of Pippenger and Spencer, proven using the R\\\"odl nibble method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-16T14:57:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N35",
      "05C70"
    ],
    "keywords": [
      "long gaps",
      "th prime",
      "fourth author",
      "hypergraph covering theorem",
      "fifth authors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5029F"
    }
  }
}