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. 1.

Abstract. We extend our previous computations to show that there are 585355 Carmichael numbers up to 1017. 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. 1.

Abstract. 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 threeprime Carmichael numbers are given, with particular reference to the conjecture of Granville and Pomerance in [10]. 1.