# Can a Turing Machine compute the binary representation of $n!$ in $O(n!)$ time?

We can compute the binary representation of $$n$$ and similarly by decrementing the value of $$n$$ by $$1$$ each time we can get all values from $$2$$ to $$n$$. We can now use a Turing Machine that multiplies binary numbers to get the value of $$n$$. But will this computation be bounded by $$O(n)$$? That is, can $$n!$$ be a time constructible function?

• – dkaeae Feb 5 '19 at 15:36
• It might be useful to mention what definition of time constructible you are referring to (there is at least a couple) as well as whether the input $n$ is given either in unary or binary. – dkaeae Feb 5 '19 at 15:37
• $n$ is given in binary. Here time constructible would refer to producing the binary representation in $O(f(n))$ time – kauray Feb 5 '19 at 15:40