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Old 2018-06-02, 09:47   #4
Romulan Interpreter
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Jun 2011

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Originally Posted by kriesel View Post
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
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