{
  "id": "1908.08613",
  "version": "v1",
  "published": "2019-08-22T22:33:17.000Z",
  "updated": "2019-08-22T22:33:17.000Z",
  "title": "Large prime gaps and probabilistic models",
  "authors": [
    "William Banks",
    "Kevin Ford",
    "Terence Tao"
  ],
  "comment": "38 pages; 1 figure",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we obtain heuristic upper and lower bounds for the size of the largest prime gap in the interval $[1,x]$. Our results are stated in terms of the extremal bounds in the interval sieve problem. The same methods also allow us to rigorously relate the validity of the Hardy-Littlewood conjectures for an arbitrary set (such as the actual primes) to lower bounds for the largest gaps within that set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T22:33:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11B83"
    ],
    "keywords": [
      "large prime gaps",
      "probabilistic model",
      "lower bounds",
      "largest prime gap",
      "random residue class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}