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2018-06-02, 09:47   #4
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

9,787 Posts

Quote:
 Originally Posted by kriesel How was that calculated?
Logarithms. I won't repeat what ET said, but just use the logarithms properties to compute the binary logarithm of 10 at the power 1M (the first number with 1M decimal digits), considering that $$\log_a x^n=n\log_a x$$ and $$\log_a x=\frac{log_b x}{log_b a}$$.

To calculate how many digits in base 5 will $$10^{1000000}$$ have, you need to compute $$\log_5 10^{1000000}$$.
To calculate how many bits will $$10^{1000000}$$ have, you need to compute $$\log_2 10^{1000000}$$. That is the power of 2 you need to raise 2 to get 10^1M (i.e a number with 1M digits). Then round it to the next prime.

Last fiddled with by LaurV on 2018-06-02 at 09:57