{
  "abstract": "Let $f\\in\\mathbb Q[t]$ be an irreducible integer-valued polynomial of positive degree with positive leading coefficient. We show that there is a constant $c_f>0$ such that, for every sufficiently large real $X$, the interval $(X/2,X]$ contains a block of at least $c_f\\log X\\log\\log X$ consecutive integers $n$ for which $f(n)$ is composite. The exponent of $\\log\\log X$ does not depend on the degree of $f$. This improves a result of Ford and Gabdullin, replacing a small fixed power of $\\log\\log X$ by $\\log\\log X$. The result includes the case $f(t)=t^2+1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10762",
  "author_total": 1,
  "authors": [
    {
      "name": "Artyom Radomskii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fv74wstnzyvec.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10762",
  "fulltext_url": null,
  "id": "fv74wstnzyvec",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10762",
  "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": "W7221106972",
  "pdf_url": "https://arxiv.org/pdf/2610.10762",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fv74wstnzyvec.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.10762",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10762"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Long intervals of consecutive composite values of polynomials",
  "title_text": "Long intervals of consecutive composite values of polynomials",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/fv74wstnzyvec",
  "venue": "arXiv",
  "versions": []
}