Leviathan Number

Author

Eric W. Weisstein
March 24, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Numbers/LeviathanNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/LeviathanNumber.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Number

Expand[(10^666)!]

FunctionExpand[%]

N[%]

Decimal Digits

FullSimplify[Normal[Series[Log[10,z!],{z,∞,0}]],z>0]/.Log[100]:>2Log[10]

Table[Length[IntegerDigits[(10^n)!]],{n,5}]

Ceiling[Table[((2 z (-1+Log[z])+Log[2 π z])/(2 Log[10]))/.z->10^n,{n,5}]]

Ceiling[((2 z (-1+Log[z])+Log[2 π z])/(2 Log[10]))/.z->(10^666)]

N[%]

Number of Trailing Zeros

kmax=Floor[Log[5,(10^666)]]

With[{n=(10^666)},Sum[Floor[n/5^k], {k, Floor[Log[5,n]]}]]

25 (10^664)-%