{
  "id": "1206.2148",
  "version": "v2",
  "published": "2012-06-11T09:51:08.000Z",
  "updated": "2012-07-28T02:49:34.000Z",
  "title": "Sumsets in primes containing almost all even positive integers",
  "authors": [
    "Ping Xi"
  ],
  "comment": "This paper has been withdrawn by the author",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $A$ be a subset of primes up to $x$. If we assume $A$ is well-distributed (in the Siegel-Walfisz sense) in any arithmetic progressions to moduli $q\\leqslant(\\log x)^c$ for any $c>0$, then the sumset $A+A$ has density 1/2 in the natural numbers as $x$ tends to infinity, which also yields almost all even positive integers could be represented as the sums of two primes in $A$ as $x$ tends to infinity. This result, improving the previous results in such special case, could be compared with the classical estimation for the exceptional set of binary Goldbach problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-28T02:49:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32",
      "11B13",
      "11P55"
    ],
    "keywords": [
      "positive integers",
      "primes containing",
      "binary goldbach problem",
      "natural numbers",
      "siegel-walfisz sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2148X"
    }
  }
}