{
  "id": "1307.1840",
  "version": "v1",
  "published": "2013-07-07T09:00:05.000Z",
  "updated": "2013-07-07T09:00:05.000Z",
  "title": "Primality test for numbers of the form $(2p)^{2^n}+1$",
  "authors": [
    "Yingpu Deng",
    "Dandan Huang"
  ],
  "comment": "15 pages, 2 tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe a primality test for number $M=(2p)^{2^n}+1$ with odd prime $p$ and positive integer $n$. And we also give the special primality criteria for all odd primes $p$ not exceeding 19. All these primality tests run in polynomial time in log$_{2}(M)$. A certain special $2p$-th reciprocity law is used to deduce our result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-07T09:00:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "odd prime",
      "primality tests run",
      "th reciprocity law",
      "special primality criteria",
      "polynomial time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1840D"
    }
  }
}