{
  "id": "math/0509095",
  "version": "v2",
  "published": "2005-09-05T13:19:52.000Z",
  "updated": "2007-03-23T13:40:38.000Z",
  "title": "A remark on an inequality for the prime counting function",
  "authors": [
    "Dietrich Burde"
  ],
  "journal": "Mathematical Inequalities and Applications Vol. 10, No. 1 (2007), 9-13",
  "categories": [
    "math.NT"
  ],
  "abstract": "We note that the inequalities $0.92 \\frac{x}{\\log(x)} <\\pi(x)< 1.11 \\frac{x}{\\log(x)}$ do not hold for all $x\\ge 30$, contrary to some references. These estimates on $\\pi(x)$ came up recently in papers on algebraic number theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-23T13:40:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05"
    ],
    "keywords": [
      "prime counting function",
      "inequality",
      "algebraic number theory",
      "references"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9095B"
    }
  }
}