{
  "id": "1606.06874",
  "version": "v1",
  "published": "2016-06-22T10:06:14.000Z",
  "updated": "2016-06-22T10:06:14.000Z",
  "title": "New bounds for the sum of the first $n$ prime numbers",
  "authors": [
    "Christian Axler"
  ],
  "comment": "27 pages, comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we establish a general asymptotic formula for the sum of the first $n$ prime numbers, which leads to a generalization of the most accurate asymptotic formula given by Massias and Robin. Further we prove a series of results concerning Mandl's inequality on the sum of the first $n$ prime numbers. We use these results to find new explicit estimates for the sum of the first $n$ prime numbers, which improve the currently best known estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-22T10:06:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L20",
      "11N37",
      "11A41"
    ],
    "keywords": [
      "prime numbers",
      "accurate asymptotic formula",
      "results concerning mandls inequality",
      "general asymptotic formula",
      "explicit estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}