The thing that was said to be impossible was writing a fast FizzBuzz. Assuming that your reference is C, it kind of is.

This has piqued my interest, I'm slightly familiar with C and Python, do you (or does anyone) know of any sort of review of resource optimisation for a simple program (like fizzbuzz)?

To me, naively, it seems like the bigend would fit in a register and so memory use wouldn't increase noticeably if you used some sort of double integer type. So it's it processor bound?

That's pretty much what BigInt is doing for you.