{
  "id": "1404.0107",
  "version": "v3",
  "published": "2014-04-01T02:09:08.000Z",
  "updated": "2014-10-11T05:18:49.000Z",
  "title": "A framework for deterministic primality proving using elliptic curves with complex multiplication",
  "authors": [
    "Alexander Abatzoglou",
    "Alice Silverberg",
    "Andrew V. Sutherland",
    "Angela Wong"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We provide a framework for using elliptic curves with complex multiplication to determine the primality or compositeness of integers that lie in special sequences, in deterministic quasi-quadratic time. We use this to find large primes, including the largest prime currently known whose primality cannot feasibly be proved using classical methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-02T11:46:03.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-11T05:18:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y11",
      "11A51",
      "11G05",
      "14K22"
    ],
    "keywords": [
      "complex multiplication",
      "deterministic primality proving",
      "elliptic curves",
      "deterministic quasi-quadratic time",
      "special sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0107A"
    }
  }
}