{
  "id": "1111.2003",
  "version": "v1",
  "published": "2011-11-08T18:25:49.000Z",
  "updated": "2011-11-08T18:25:49.000Z",
  "title": "Reducing the number of prime factors of long $κ$-tuples",
  "authors": [
    "C. S. Franze"
  ],
  "comment": "15 pages, submitted to London Mathematical Society",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that there are infinitely many integers $n$ such that the total number of prime factors of $(n+h_{1})(n+h_{2})...(n+h_{\\kappa})$ is at most $(1/2)\\kappa\\log\\kappa+O(\\kappa)$, provided $\\kappa$ is sufficiently large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-08T18:25:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N35",
      "11N36"
    ],
    "keywords": [
      "prime factors",
      "total number",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.2003F"
    }
  }
}