Calculate factorials in C#

Question

How can you calculate large factorials using C#? Windows calculator in Win 7 overflows at Factorial (3500). As a programming and mathematical question I am interested in kno

Answer 1

There exist sophisticated computational algorithms for efficiently computing the factorials of large, arbitrary precision numbers. The Schönhage–Strassen algorithm, for instance, allows you to perform asymptotically fast multiplication for arbitrarily large integers.

Case in point, Mathematica computes 22000! on my machine in less than 1 second. The Implementation Notes page at reference.wolfram.com states:

(Mathematica's) n! uses an O(log(n) M(n)) algorithm of Schönhage based on dynamic decomposition to prime powers.

Unfortunately, the implementation of such algorithms is both complicated and error prone. Rather than trying to roll your own implementation, it may be wiser for you to license a copy of Mathematica (or a similar product that meets your functional and performance needs) and either use it, or a .NET programming interface to it, to perform your computation.