{
  "abstract": "We develop explicit prime-recovery formulas from the values $Φ_n(2)$ of cyclotomic polynomials. Binary divisibility patterns detect repeated prime factors and identify the least prime divisor of a squarefree index, while small corrections to $\\log_2Φ_n(2)$ allow successive recovery of the distinct prime factors. Specializing the index gives identities for prime products and the least prime above a given integer. The same mechanism extends from finite factorizations to an infinite prime sequence: a normalized limit of cyclotomic values along the odd primorials defines a real constant $Ω=0.25061403238015047218\\ldots$, from which every odd prime can be recovered by a recursive rounding rule.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18480",
  "author_total": 1,
  "authors": [
    {
      "name": "Joseph M. Shunia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2snpz2tv0rv5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18480",
  "fulltext_url": null,
  "id": "2snpz2tv0rv5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18480",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213518509",
  "pdf_url": "https://arxiv.org/pdf/2609.18480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2snpz2tv0rv5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cyclotomic Prime Extractors",
  "title_text": "Cyclotomic Prime Extractors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/2snpz2tv0rv5s",
  "venue": "arXiv",
  "versions": []
}