Speaking of Karatsuba, in 1993 I wrote a C++ big integer package and used Karatsuba. I had some questions about how to use it when the two numbers being multiplied are not the same length. I did some experiments, and noticed hints at some patterns in the data I was seeing. I asked about this on sci.math, but as far as I know no one ever gave an explanation.

If anyone is curious and wants to figure this out, here's my old sci.math post [1].

[1] https://groups.google.com/d/msg/sci.math/MX3MLCQ0zzA/XTqUoZk...