{
  "id": "2408.03803",
  "version": "v1",
  "published": "2024-08-07T14:30:44.000Z",
  "updated": "2024-08-07T14:30:44.000Z",
  "title": "Poisson Approximation of prime divisors of shifted primes",
  "authors": [
    "Kevin Ford"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and actual prime factors of shifted primes, and apply it to show that the prime factors of shifted primes in disjoint sets behave like independent Poisson variables. As a consequence, we establish a transference principle between the anatomy of random integers up to x and of random shifted primes p+a with p < x.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-07T14:30:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N25",
      "11N35",
      "11K65"
    ],
    "keywords": [
      "prime divisors",
      "poisson approximation",
      "total variation distance estimate",
      "disjoint sets behave",
      "independent poisson variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}