[FartyMcFarter]

I think you can calculate "2^X mod (10^N)" where N is the number of digits using a modular exponentiation algorithm.

This would avoid using a lot of memory, and it would also be faster.

[nneonneo]

I am already doing that (thanks to `pow(x, y, z)` in Python). The numbers I'm working with would have trillions of digits were it not for this trick - way more than 1GB. 1GB is what I use to store all of the candidates, in an inefficient JSON format.