✔ 最佳答案
If you don't really need an exact number for that, Stirling's give you a pretty good approximation :)
http://mathworld.wolfram.com/StirlingsApproximation.html
1,000,000! ~= e^(1,000,000 ln 1,000,000 - 1,000,000)
In this way, it is possible to count the number of digits in the number.