{
  "id": "1504.04347",
  "version": "v1",
  "published": "2015-04-16T19:18:52.000Z",
  "updated": "2015-04-16T19:18:52.000Z",
  "title": "On Selberg's approximation to the twin prime problem",
  "authors": [
    "R. Balasubramanian",
    "Priyamvad Srivastav"
  ],
  "comment": "34 pages, sage program code included in the document",
  "categories": [
    "math.NT"
  ],
  "abstract": "In his Classical approximation to the Twin prime problem, Selberg proved that for $x$ sufficiently large, there is an $n \\in (x,2x)$ such that $2^{\\Omega(n)}+2^{\\Omega(n+2)} \\leq \\lambda$ with $\\lambda=14$, where $\\Omega(n)$ is the number of prime factors of $n$ counted with multiplicity. This enabled him to show that $n(n+2)$ has atmost $5$ prime factors, with one having atmost $2$ and the other having atmost $3$ prime factors, for infinitely many $n$. By using a refinement suggested by Selberg, we improve this value of $\\lambda$ to about $\\lambda=12.59$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-16T19:18:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "twin prime problem",
      "selbergs approximation",
      "prime factors",
      "classical approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404347B"
    }
  }
}