{
  "id": "1408.5110",
  "version": "v1",
  "published": "2014-08-21T18:57:27.000Z",
  "updated": "2014-08-21T18:57:27.000Z",
  "title": "Large gaps between primes",
  "authors": [
    "James Maynard"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that there exists pairs of consecutive primes less than $x$ whose difference is larger than $t(1+o(1))(\\log{x})(\\log\\log{x})(\\log\\log\\log\\log{x})(\\log\\log\\log{x})^{-2}$ for any fixed $t$. Our proof works by incorporating recent progress in sieve methods related to small gaps between primes into the Erdos-Rankin construction. This answers a well-known question of Erdos.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-21T18:57:27.000Z"
    }
  ],
  "resources": [
    {
      "type": "posts",
      "source": "Quanta Magazine",
      "title": "Prime Gap Grows After Decades-Long Lull",
      "href": "https://www.quantamagazine.org/20141210-prime-gap-grows-after-decades-long-lull/",
      "status": "public"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N35"
    ],
    "keywords": [
      "large gaps",
      "well-known question",
      "erdos-rankin construction",
      "small gaps",
      "proof works"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5110M"
    }
  }
}