{
  "id": "1705.02485",
  "version": "v1",
  "published": "2017-05-06T14:09:45.000Z",
  "updated": "2017-05-06T14:09:45.000Z",
  "title": "Primitive root discrepancy for twin primes",
  "authors": [
    "Stephan Ramon Garcia",
    "Elvis Kahoro",
    "Florian Luca"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Numerical evidence suggests that for only about $2\\%$ of pairs $p,p+2$ of twin primes, $p+2$ has more primitive roots than does $p$. If this occurs, we say that $p$ is exceptional (there are only two exceptional pairs with $5 \\leq p \\leq 10{,}000$). Assuming the Bateman-Horn conjecture, we prove that at least $0.47\\%$ of twin prime pairs are exceptional and at least $65.13\\%$ are not exceptional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-06T14:09:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11A41",
      "11N36",
      "11N37"
    ],
    "keywords": [
      "primitive root discrepancy",
      "twin prime pairs",
      "exceptional pairs",
      "bateman-horn conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}