The Carmichael numbers up to 10¹⁵

Author:

Pinch R. G. E.

Abstract

There are 105212 Carmichael numbers up to 10 15 {10^{15}} : we describe the calculations. The numbers were generated by a back-tracking search for possible prime factorizations, and the computations checked by searching selected ranges of integers directly using a sieving technique, together with a "large-prime variation".

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference28 articles.

1. There are infinitely many Carmichael numbers;Alford, W. R.;Ann. of Math. (2),1994

2. On composite numbers 𝑛 for which 𝑎ⁿ⁻¹≡(𝑚𝑜𝑑𝑛) for every 𝑎 prime to 𝑛;Beeger, N. G. W. H.;Scripta Math.,1950

3. Note on a new number theory function;Carmichael, R. D.;Bull. Amer. Math. Soc.,1910

4. On Composite Numbers 𝑃 Which Satisfy the Fermat Congruence 𝑎^{𝑃-1}≡1𝑚𝑜𝑑𝑃;Carmichael, R. D.;Amer. Math. Monthly,1912

5. I. Damgård and P. Landrock, Improved bounds for the Rabin primality test, preprint, 12 March 1992, Coding and Cryptography III, Proc. 3rd IMA Conf. on Coding and Cryptography (M. Ganley, ed.), Cirencester, December 1991 (to appear).

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