{
  "id": "0711.3940",
  "version": "v2",
  "published": "2007-11-26T05:18:30.000Z",
  "updated": "2008-10-05T21:03:04.000Z",
  "title": "A recursion equation for prime numbers",
  "authors": [
    "Joseph B. Keller"
  ],
  "comment": "2 pages; replacement 10/05/2008 corrects typographical error page 2, reference #1, author last name",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is shown that the first $n$ prime numbers $p_1,...,p_n$ determine the next one by the recursion equation $$ p_{n+1} =\\lim\\limits_{s\\to +\\infty} [\\prod\\limits^n_{k=1} (1-\\frac{1}{p^s_k}) \\sum\\limits^\\infty_{j=1} \\frac{1}{j^s} -1]^{-1/s}. $$ The upper limit on the sum can be replaced by $2p_n -1$, and the result still holds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-05T21:03:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A41"
    ],
    "keywords": [
      "prime numbers",
      "recursion equation",
      "upper limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3940K"
    }
  }
}