Classification of Carmichael numbers

The classification of Carmichael numbers into classes A, B1 and B2 is described in [1].

Note that Table 3 in this paper is about atomic Carmichael numbers up to 10²⁴, and on this page we report on all Carmichael numbers up to 10²⁴. See Carmichael numbers that are products of Carmichael numbers for the non-atomic Carmichael numbers up to 10²⁴.

Files to download

All Carmichael numbers up to 10²⁴ (as found on Jon Webster's website, look for new_table.txt) are distributed over 342 files carmichaels_k_d_c.txt, where

k = number of prime factors,
d = number of digits,
c = class.

The 342 files come compressed into three big files, one per class:

carmichaels_A.7z: 141 files, compressed: 1.08 GB, decompressed: 3.63 GB,
carmichaels_B1.7z: 143 files, compressed: 1.08 GB, decompressed: 3.62 GB,
carmichaels_B2.7z: 58 files, compressed: 4.10 MB, decompressed: 11.7 MB.

Statistics

Counts per class, number of prime factors k, and number of digits d:

Counts per class, number of prime factors k, and h:

Reference

[1] Alejandra Alcantarilla Sánchez, Jolijn Cottaar, Tanja Lange, and Benne de Weger, Ours go to 211: Euler pseudoprimes to 47 prime bases (from Carmichael numbers), submitted.

Authors

Alejandra Alcantarilla Sánchez, Jolijn Cottaar, Tanja Lange, and Benne de Weger, Eindhoven University of Technology, Eindhoven, The Netherlands.
January 25, 2026