{
  "id": "math/0106223",
  "version": "v1",
  "published": "2001-06-26T20:57:20.000Z",
  "updated": "2001-06-26T20:57:20.000Z",
  "title": "Discrete Reanalysis of a New Model of the Distribution of Twin Primes",
  "authors": [
    "P. F. Kelly",
    "Terry Pilling"
  ],
  "comment": "8 pages, 3 figures, LaTeX",
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently we have introduced a novel characterisation of the distribution of twin primes that consists of three essential elements. These are: that the twins are most naturally viewed as a subsequence of the primes themselves, that the likelihood of a particular prime in sequence being the first element of a twin is akin to a fixed-probability random event, and that this probability varies with $\\pi_{1}$, the count of primes up to this number, in a simple way. Our initial studies made use of two unproven assumptions: that it was consistent to model this fundamentally discrete system with a continuous probability density, and that the fact that an upper-bound cut-off for prime separations exists could be consistently ignored in the continuous analysis. The success of the model served as a posteriori justification for these assumptions. Here we perform the analysis using a discrete formalism -- not passing to integrals -- and explicitly include a self-consistently defined cut-off. In addition, we reformulate the model so as to minimise the input data needed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-26T20:57:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05"
    ],
    "keywords": [
      "twin primes",
      "discrete reanalysis",
      "distribution",
      "fixed-probability random event",
      "first element"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6223K"
    }
  }
}