What digits does googol!
arithmetic/digits/most.significant/googol
Problem
What digits does googol! start with?
Show solution
I'm not sure how to calculate the first googol of digits of log10(e), but
here's the first 150(approximately) of them...
0.43429448190325182765112891891660508229439700580366656611445378316586464920
8870774729224949338431748318706106744766303733641679287158963906569221064663
We need to deal with the digits immediately after the decimal point in
googol*log10(e), which are .187061
frac[log(googol!)] = frac[halflog2pi + 50 + googol(100-log10(e))]
= frac{halflog2pi + frac[googol(100-log10(e))]}
= frac[.399090 + (1- .187061)]
= .212029
10 ** .212029 = 1.629405
Which means that googol! starts with 1629