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^{n} = n log n < n^{2}
So n! always has fewer than n^{2} digits (except for 1! and 0!).
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
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Re: Arithmetic puzzle
Alright then. Bye.
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Re: Arithmetic puzzle
houlahop wrote: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?
I would guess that interpretation is lim(n>infinity) (n^2)/(d(n!)*pi(n))=1.
What is the function d in this case?
Re: Arithmetic puzzle
I believe d(n) is just shorthand for "the number of digits in n."
I wonder about the fact that n^2 and pi(n) are not dependent on the base, but d(n) is.
I wonder about the fact that n^2 and pi(n) are not dependent on the base, but d(n) is.
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