A googolplex expressed in factorial form?

1. Feb 6, 2016

Saracen Rue

Does anybody know what the factorial form of a googolplex would be?

2. Feb 6, 2016

Mentallic

So you're asking to calculate the inverse gamma function, since the gamma function and the factorial are closely related. i.e. you want to solve for n in
$$n!=10^{10^{100}}$$

I can give you a quick start on the approximate magnitude of n. Since a crude approximation is $n!\approx n^n$, then choosing $n=10^{100}$ gives us
$$n^n=\left(10^{100}\right)^{\left(10^{100}\right)}=10^{100\times 10^{100}}=10^{10^{102}}\approx 10^{10^{100}}$$

hence n is somewhere in the ballpark of a googol.

Unless of course, you meant something else by your OP. Maybe you were asking what $$10^{10^{100}}!$$ is?

3. Feb 6, 2016

Saracen Rue

Yes I was asking what 'n' would have been, and thank you for helping.

4. Feb 6, 2016

Bill_Nye_Fan

I tried to get Wolfram Alpha to solve but it exceeded the standard calculation time - maybe someone with a pro account can try it.

Anyway just through guessing I managed to get 102483838377090000000000000000000000000000000000000000000000000000000000000000000000000000000000000! (1.0248383837709e+98!) as an answer.

Last edited: Feb 6, 2016