{
  "id": "math/0505300",
  "version": "v1",
  "published": "2005-05-14T05:28:56.000Z",
  "updated": "2005-05-14T05:28:56.000Z",
  "title": "Small Gaps between Primes Exist",
  "authors": [
    "D. A. Goldston",
    "Y. Motohashi",
    "J. Pintz",
    "C. Y. Yildirim"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In the recent preprint [3], Goldston, Pintz, and Y{\\i}ld{\\i}r{\\i}m established, among other things, $$ \\liminf_{n\\to\\infty}{p_{n+1}-p_n\\over\\log p_n}=0,\\leqno(0) $$ with $p_n$ the $n$th prime. In the present article, which is essentially self-contained, we shall develop a simplified account of the method used in [3]. While [3] also includes quantitative versions of $(0)$, we are concerned here solely with proving the qualitative $(0)$, which still exhibits all the essentials of the method. We also show here that an improvement of the Bombieri--Vinogradov prime number theorem would give rise infinitely often to bounded differences between consecutive primes. We include a short expository last section. Detailed discussions of quantitative results and a historical review will appear in the publication version of [3] and its continuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-14T05:28:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11P32"
    ],
    "keywords": [
      "small gaps",
      "bombieri-vinogradov prime number theorem",
      "th prime",
      "short expository",
      "publication version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5300G"
    }
  }
}