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

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

2007-11-19

arxiv.org/abs/0711.2915v2

Mathematics

Number Theory

37 pages; 5 tables; amended version contains a minor factual correction on page 25 immediately before Challenge 4, an updated

Scientific paper

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 $10^{24}$. 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].

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