The number (10^(666))! where 666 is the beast number and
"!" denotes a factorial is called Leviathan Number.
Given that this number has approximately 6.656×10^(668) decimal digits, evaluate the number of its trailing zeros.
The number of zeros is the number of factors of 5. This is always smaller than 1/5 + 1/25 + 1/125 + 1/625 + ... = 1/4
and for large numbers, this estimate is quite good.
For example
1000! has exactly 200+40+8+1=249 trailing zeros and 1/4 of 1000 is only greater by 1.
A good approximation then is 1/4 of 10^666 or 2.5*10^665
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Posted by Jer
on 2017-11-10 08:34:45 |
Good approximation, upper bound
