Tuesday, August 24, 2010

Carmichael Numbers with Exactly k Prime Factors

One of my projects for this year is to finish a paper that Red Alford and I started where we show the existence of Carmichael numbers with exactly k prime factors for a wide range of k.  Red passed away 7 years ago, so I think it's about time I get this paper out of the door.

One of my problems has been with the complexity of the code needed to finish the computation.  Recently I've been teaching myself Python, which looks like it can cut through some of the complexity issues for the less computationally-intensive parts of the computation.

Anyway, I recently received a request for information about the technique Red and I used.  I realized that I never put any of my talks about this technique on-line, so I uploaded a talk I gave in 2003 at the Hugh Williams conference in Banff.