{
  "id": "math/0607588",
  "version": "v1",
  "published": "2006-07-24T09:24:05.000Z",
  "updated": "2006-07-24T09:24:05.000Z",
  "title": "A Small World Network of Prime Numbers",
  "authors": [
    "Anjan Kumar Chandra",
    "Subinay Dasgupta"
  ],
  "comment": "6 pages, 10 figures",
  "journal": "Physica A 357 (2005) 436",
  "doi": "10.1016/j.physa.2005.02.089",
  "categories": [
    "math.NT",
    "cond-mat.stat-mech"
  ],
  "abstract": "According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers : $n = p + q$. We construct a network where each node is a prime number and corresponding to every even number $n$, we put a link between the component primes $p$ and $q$. In most cases, an even number can be broken up in many ways, and then we chose {\\em one} decomposition with a probability $|p - q|^{\\alpha}$. Through computation of average shortest distance and clustering coefficient, we conclude that for $\\alpha > -1.8$ the network is of small world type and for $\\alpha < -1.8$ it is of regular type. We also present a theoretical justification for such behaviour.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-24T09:24:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prime number",
      "small world network",
      "average shortest distance",
      "small world type",
      "component primes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}