Skip to content
DraconiticResearch
Search Sources API
194,220 studies31 sourcesUpdated 27 min ago
PreprintCC BY 4.0arXiv

The Prime Wavelet Tree: Compressing the Carmichael Numbers

  • Ankur Gupta
  • Jonathan Webster
  • Sylvia Webster
Open at sourcePDFDOICite

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 1024 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.

Related

  1. On Carmichael Numbers Constructed from Consecutive Jacobsthal Numbers
    Hayat Bensella
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Compressing multivariate functions with tree tensor networks
    Joseph Tindall, Miles Stoudenmire, Ryan Levy
    SciPost PhysicsPeer-reviewedCC BY 4.0Full text21 citedNumerical analysis & scientific computingCrossrefOpenAlex
  3. A Note on Carmichael Numbers of the form $ N=(d+1)(3d+1)(4d+1)$
    Hayat Bensella
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. A Korselt Characterization of Carmichael Numbers of the Form (aCn+1)(aCn+1+1)(aCn+2+1)
    Hayat Bensella
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Idempotence in Carmichael and Giuga numbers and its application to the Agoh-Giuga conjecture
    Miguel Ángel López
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{gupta2026prime,
  title = {{The Prime Wavelet Tree: Compressing the Carmichael Numbers}},
  author = {Ankur Gupta and Jonathan Webster and Sylvia Webster},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02550},
  eprint = {2610.02550},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02550},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Prime Wavelet Tree: Compressing the Carmichael Numbers
AU  - Ankur Gupta
AU  - Jonathan Webster
AU  - Sylvia Webster
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02550
UR  - https://arxiv.org/abs/2610.02550
AB  - 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.
ER  -