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How Triple Powers of Integers Begin and End

​
x
77
y
77
z
77
begins
107153936179743175615852800097163877852859988946339
length
34311563841186728066105289695648190510153388
ends
80233555561937255712407650378894872221968013587197
z
y
x
77
77
77
length of the length is 146 digits
A googol is
100
10
, and a googolplex is
100
10
10
.
What is
5
5
5
? With base 10 logarithms, the length of this enormous number can be calculated:
5
5
log
10
5=2184.281264...
. Rounding up the part before the decimal point gives the length as 2185 digits. Let the part after the decimal point be
a=.281264…
, then the digits of
a
10
give the start of the enormous number, 1911….
With modulus methods, the ends of huge numbers can also be calculated. This Demonstration uses both logs and modulus methods to give glimpses at enormous numbers bigger than a googolplex.
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