{
  "id": "1802.02470",
  "version": "v1",
  "published": "2018-02-07T15:15:12.000Z",
  "updated": "2018-02-07T15:15:12.000Z",
  "title": "On the gaps between consecutive primes",
  "authors": [
    "Yu-Chen Sun",
    "Hao Pan"
  ],
  "comment": "This is a very very preliminary draft, which maybe contains some mistakes",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $p_n$ denote the $n$-th prime. For any $m\\geq 1$, there exist infinitely many $n$ such that $p_{n}-p_{n-m}\\leq C_m$ for some large constant $C_m>0$, and $$p_{n+1}-p_n\\geq \\frac{c_m\\log n\\log\\log n\\log\\log\\log\\log n}{\\log\\log\\log n}, $$ for some small constant $c_m>0$. Furthermore, we also obtain a related result concerning the least primes in arithmetic progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-07T15:15:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "consecutive primes",
      "arithmetic progressions",
      "small constant",
      "th prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}