The Carmichael numbers up to 10¹⁸

2006/04/17 by Richard G. E. Pinch, Pinch, Richard G. E.
Mathematics · #11-04 #11A51 #11Y11 #11Y99 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11-04 #msc:11A51 #msc:11Y11 #msc:11Y99

paper · pdf · doi:10.48550/arxiv.math/0604376

11 pages, 2 figures

arxiv created 2006/04/17 · arxiv updated 2009/12/01

Abstract

We extend our previous computations to show that there are 1401644 Carmichael numbers up to 10¹⁸. 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.

Related

• The Carmichael numbers up to 10¹⁷
• The Carmichael numbers up to 10¹⁶
• Carmichael number variable relations: three-prime Carmichael numbers up to 10²4
• Advances in Tabulating Carmichael Numbers
• On the Classification and Algorithmic Analysis of Carmichael Numbers