{
  "id": "1008.2381",
  "version": "v2",
  "published": "2010-08-13T19:57:25.000Z",
  "updated": "2010-08-31T19:17:33.000Z",
  "title": "Note On Prime Gaps And Very Short Intervals",
  "authors": [
    "N. A. Carella"
  ],
  "comment": "12 Pages, 1 Table, Improved",
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the Riemann hypothesis, this article discusses a new elementary argument that seems to prove that the maximal prime gap of a finite sequence of primes p_1, p_2, ..., p_n <= x, satisfies max {p_(n+1) - p_n : p_n <= x} <= c1((logx)^2)/loglogx, c1 > 0 constant. Equivalently, it shows that the very short intervals (x, x + y] contain prime numbers for all y > c2((logx)^2)/loglogx, c2 > 0 constant, and sufficiently large x > 0.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-31T19:17:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11A41",
      "11P32"
    ],
    "keywords": [
      "short intervals",
      "contain prime numbers",
      "maximal prime gap",
      "article discusses",
      "finite sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2381C"
    }
  }
}