{
  "id": "2405.05727",
  "version": "v2",
  "published": "2024-05-09T12:41:33.000Z",
  "updated": "2024-05-13T12:22:42.000Z",
  "title": "On Chen's theorem, Goldbach's conjecture and almost prime twins",
  "authors": [
    "Runbo Li"
  ],
  "comment": "19 pages. Chen's double sieve is applied and some calculation errors are corrected. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $N$ denotes a sufficiently large even integer, we define $D_{1,2}(N)$ as the same as those in previous articles about Chen's theorem. In this paper, we show that $D_{1,2}(N) \\geqslant 1.267 \\frac{C(N) N}{(\\log N)^2}$, improving previous record of Wu about $40\\%$. We also get similar results on twin prime problem and additive representations of integers. An important step in the proof is the application of a theorem of Lichtman.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-05-13T12:22:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chens theorem",
      "goldbachs conjecture",
      "prime twins",
      "twin prime problem",
      "important step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}