{
  "abstract": "We establish two quantitative results concerning additive decompositions of the set $\\mathbb{P}$ of primes. First, we prove that, if $A,B\\subseteq\\mathbb N$ have at least two elements and $A+B$ differs from the primes by only finitely many elements, then $$ \\frac{\\sqrt{x}}{\\log x}\\ll A(x),B(x) \\ll \\sqrt{x}. $$ Second, we show that, if $A,B,C\\subseteq\\mathbb N$ have at least two elements each, then $$ ((A+B+C)\\mathbin{\\bigtriangleup}\\mathbb P)(x) \\gg \\frac{\\sqrt{x}}{(\\log x)^2}. $$ An analogous estimate is obtained for sumsets of $k\\ge 3$ sets. The proofs use Montgomery's large sieve, Gallagher's larger sieve, a mean-value argument for a certain multiplicative function, and a submultiplicative sumset inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15758",
  "author_total": 1,
  "authors": [
    {
      "name": "Paolo Leonetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0n7frtjzt323m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15758",
  "fulltext_url": null,
  "id": "0n7frtjzt323m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15758",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221775069",
  "pdf_url": "https://arxiv.org/pdf/2610.15758",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0n7frtjzt323m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15758",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15758"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the inverse Goldbach problem",
  "title_text": "On the inverse Goldbach problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0n7frtjzt323m",
  "venue": "arXiv",
  "versions": []
}