{
  "id": "1606.08690",
  "version": "v1",
  "published": "2016-06-28T13:33:31.000Z",
  "updated": "2016-06-28T13:33:31.000Z",
  "title": "On the number of prime factors of Mersenne numbers",
  "authors": [
    "Abílio Lemos",
    "Ady Cambraia Junior"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $n$ a positive integer, $M_n=2^n-1$ the $n$th Mersenne number and $\\omega(n)$ the number of distinct prime divisors of $n$. We present a description of the Mersenne numbers satisfying $\\omega(M_n)\\leq3$. Moreover, we prove that the inequality, for $\\epsilon>0$, $\\omega(M_n)> 2^{(1-\\epsilon)\\log\\log n} -3 $ holds almost all positive integer $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-28T13:33:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prime factors",
      "th mersenne number",
      "positive integer",
      "distinct prime divisors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}