The Carmichael numbers up to $10^{18}$

Publication date: 17 April 2006

Abstract: We extend our previous computations to show that there are 1401644 Carmichael numbers up to

1 0^{18}

. As before, the numbers were generated by a back-tracking search for possible prime factorisations together with a ``large prime variation. We present further statistics on the distribution of Carmichael numbers.

Has companion code repository: https://github.com/ditekunov/Purity-Project

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to number theory (11-04) Factorization; primality (11A51) Computational number theory (11Y99) Primality (11Y11)

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