English

Carmichael number variable relations: three-prime Carmichael numbers up to 10^24

Number Theory 2008-02-27 v2

Abstract

Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implementation up to 102410^{24}. Statistics relevant to the distribution of three-prime Carmichael numbers are given, with particular reference to the conjecture of Granville and Pomerance in [A.Granville and C.Pomerance, Two contradictory conjectures concerning Carmichael numbers, Math. Comp. 71 (2001), 883-908].

Keywords

Cite

@article{arxiv.0711.2915,
  title  = {Carmichael number variable relations: three-prime Carmichael numbers up to 10^24},
  author = {J. M. Chick},
  journal= {arXiv preprint arXiv:0711.2915},
  year   = {2008}
}

Comments

37 pages; 5 tables; amended version contains a minor factual correction on page 25 immediately before Challenge 4, an updated reference and 6 very minor textual improvements

R2 v1 2026-06-21T09:44:49.369Z