If you want to use huge factorials for practical calculations related to the magnitude of the number, rather than as a demonstration of being able to exactly determine every digit of such a factorial, then a relatively fast way to do such things in Perl is Math::BigApprox.

Computing 2032597! still takes a while because it actually does the 2 million multiplications and, although Math::BigApprox operations are about 10x faster than Math::BigInt operations (even when using GMP, same for bignum) and don't fail for this case, they are still about 20x slower than vanilla Perl math operations here.

 % perl -MMath::BigApprox=c -e'$s= time(); $f= !c(203259); print $f, $
+/, time()-$s," seconds\n"'
4.81043e+990637
14 seconds
% perl -MMath::BigApprox=c -e'$s= time(); $f= !c(2032597); print $f, $
+/, time()-$s," seconds\n"'
1e+11938984
133 seconds
[download]

Not an ideal solution, but perhaps an option you weren't aware of.