{
  "abstract": "We present two number-theoretic compression techniques. The first is \\textit{local}, and compresses individual numbers. The second is \\textit{global}, and compresses the entire set of numbers using a \\textit{prime wavelet tree}, which is a data structure of independent interest. Our techniques apply to any set of numbers satisfying a Korselt-like criterion. We demonstrate our compression techniques using the recently completed tabulation of all $308{,}279{,}939$ Carmichael numbers less than $10^{24}$ that occupies $18.4$ gigabytes as text. When combined with standard compression techniques and a heuristic choice of divisors, the resulting file is $588.7$ megabytes ($31.2$ times smaller than the text file). The initial $80$-bit numbers now use about $15.3$ bits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02550",
  "author_total": 3,
  "authors": [
    {
      "name": "Ankur Gupta"
    },
    {
      "name": "Jonathan Webster"
    },
    {
      "name": "Sylvia Webster"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/498ghdqsevcc5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02550",
  "fulltext_url": null,
  "id": "498ghdqsevcc5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02550",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1702|Algorithms and Data Compression"
    ]
  ],
  "openalex": "W7220413541",
  "pdf_url": "https://arxiv.org/pdf/2610.02550",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/498ghdqsevcc5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02550",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02550"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Prime Wavelet Tree: Compressing the Carmichael Numbers",
  "title_text": "The Prime Wavelet Tree: Compressing the Carmichael Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/498ghdqsevcc5",
  "venue": "arXiv",
  "versions": []
}