22!=1124000727777607680000

The number 22! is a 22 digit number

11240

00727

77760

76800

00

Find a number n such as n! is n^2 digit number

More generally find n such as n! is n^k digit number (k>2)

## Arithmetic puzzle

**Moderators:** jestingrabbit, Moderators General, Prelates

### Re: Arithmetic puzzle

It is not possible.

For n>1 we have:

log n! < log n

So n! always has fewer than n

For n>1 we have:

log n! < log n

^{n}= n log n < n^{2}So n! always has fewer than n

^{2}digits (except for 1! and 0!).### Re: Arithmetic puzzle

Thank you

(n^2)/d(n!) is equal to pi(n) when n goes to infinity (where pi(n) is the counting function of primes)

Is there any interpretation of this "equality"?

My last post because I wanted to point out to this.

Good luck and good bye!

To the moderator :

No one asked me about clarification. Sir Gabriel answered without asking.

Conclusion : Either you did not read the post, either you are lying.

Where did you see any contempt from myself?

(n^2)/d(n!) is equal to pi(n) when n goes to infinity (where pi(n) is the counting function of primes)

Is there any interpretation of this "equality"?

My last post because I wanted to point out to this.

Good luck and good bye!

To the moderator :

No one asked me about clarification. Sir Gabriel answered without asking.

Conclusion : Either you did not read the post, either you are lying.

Where did you see any contempt from myself?

- SecondTalon
- SexyTalon
**Posts:**25485**Joined:**Sat May 05, 2007 2:10 pm UTC**Location:**Louisville, Kentucky, USA, Mars. HA!-
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### Re: Arithmetic puzzle

Alright then. Bye.

heuristically_alone wrote:I want to write a DnD campaign and play it by myself and DM it myself.

heuristically_alone wrote:I have been informed that this is called writing a book.

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