Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 44 min ago
PreprintCC BY-NC-ND 4.0arXiv

Cyclotomic Prime Extractors

  • Joseph M. Shunia
Open at sourcePDFDOICite

Abstract

We develop explicit prime-recovery formulas from the values Φn(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 log2Φn(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…, from which every odd prime can be recovered by a recursive rounding rule.

Related

  1. Unsupported Cyclotomic Divisors in Three-Prime Integer Tilings
    Hu Tan, Ying Zhang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Primary components and large prime factors of cyclotomic values
    Wei Xie
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Quadratic Extractors
    Gautam Chandrasekaran, Jesse Goodman, David Zuckerman
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  4. Non-Malleable Affine Extractors with Small Error and Complexity Lower Bounds
    Xin Li, Yan Zhong
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. Post-critically finite polynomials over cyclotomic closures of number fields
    Patrick Ingram, Jorge Mello
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{shunia2026cyclotomic,
  title = {{Cyclotomic Prime Extractors}},
  author = {Joseph M. Shunia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18480},
  eprint = {2609.18480},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18480},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Cyclotomic Prime Extractors
AU  - Joseph M. Shunia
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18480
UR  - https://arxiv.org/abs/2609.18480
AB  - 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…, from which every odd prime can be recovered by a recursive rounding rule.
ER  -