{
  "id": "1603.03720",
  "version": "v1",
  "published": "2016-03-11T18:41:06.000Z",
  "updated": "2016-03-11T18:41:06.000Z",
  "title": "Unexpected biases in the distribution of consecutive primes",
  "authors": [
    "Robert J. Lemke Oliver",
    "Kannan Soundararajan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "While the sequence of primes is very well distributed in the reduced residue classes $\\pmod q$, the distribution of pairs of consecutive primes among the permissible $\\phi(q)^2$ pairs of reduced residue classes $\\pmod q$ is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared to numerical data, and the observed fit is very good.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-11T18:41:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "consecutive primes",
      "unexpected biases",
      "reduced residue classes",
      "distribution",
      "conjectural explanation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}