Is there any efficient algorithm for counting number of digits in n! without actually calculating n!?
[Addendum -- PLC]: I voted to close the question as "no longer relevant" because of Gerry's answer that one could just use Stirling's formula, as supplemented by a comment which referred to a formula of Kamenetsky given on the online journal of integer sequences. It seems now that it is an open question whether Kamenetsky's formula always (rather than just "most of the time") gives exactly the right answer, so there is more here than I had realized. A followup question which provides more context has been asked here: