{
  "id": "math/0604376",
  "version": "v1",
  "published": "2006-04-17T20:28:06.000Z",
  "updated": "2006-04-17T20:28:06.000Z",
  "title": "The Carmichael numbers up to $10^{18}$",
  "authors": [
    "Richard G. E. Pinch"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend our previous computations to show that there are 1401644 Carmichael numbers up to $10^{18}$. As before, the numbers were generated by a back-tracking search for possible prime factorisations together with a ``large prime variation''. We present further statistics on the distribution of Carmichael numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-17T20:28:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y99",
      "11A51",
      "11Y11",
      "11-04"
    ],
    "keywords": [
      "carmichael numbers",
      "large prime variation",
      "prime factorisations",
      "back-tracking search"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4376P"
    }
  }
}