{
  "id": "1507.07028",
  "version": "v1",
  "published": "2015-07-24T21:43:02.000Z",
  "updated": "2015-07-24T21:43:02.000Z",
  "title": "On the Difference between Consecutive Primes and Estimates of the Number of Primes in the Interval $(n, 2n)$",
  "authors": [
    "Felix Sidokhine"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Using evaluations of the difference between consecutive primes we develop another way of estimating of the number of primes in the interval $(n, 2n)$. We also discuss the ultra Cramer conjecture, $p_{n+1} - p_n = O(log^{1+\\epsilon}p_n)$ where $\\epsilon > 0$, in the context of the results we have obtained in our paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-24T21:43:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "consecutive primes",
      "difference",
      "ultra cramer conjecture",
      "evaluations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150707028S"
    }
  }
}