[crashocaster]

For some large n, integers in the algorithm may be so large that operations on them cease to be constant time.

[d0mine]

that is obvious. But how does it change big O? (why any manual implementation would have a better big O compared to existing arithmetics implementation in CPython?)

[kaba0]

I think he meant that naively implementing an algorithm may not be bounded by the O notation he/she originally wanted due to code calling other functions “hidden” from the programmer.