Carmichael number variable relations: three-prime Carmichael numbers up to 10^24
J. M. Chick

TL;DR
This paper reviews bounds related to Carmichael numbers, introduces a new algorithm for finding three-prime Carmichael numbers up to 10^24, and discusses their distribution in relation to existing conjectures.
Contribution
A new algorithm for identifying three-prime Carmichael numbers and extended bounds and statistics up to 10^24.
Findings
Distribution of three-prime Carmichael numbers analyzed
Algorithm successfully implemented up to 10^24
Insights into conjectures by Granville and Pomerance
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 . 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].
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · graph theory and CDMA systems
