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The problem is to calculate the distribution of digits $0-9$ of $2^{4000}$, and the interesting result shows that it is almost a random distribution with almost equally $10\%$ of each digit. After that, I tested $2^{5000}$, $2^{6000}$, and so on, the same result applied too. So I guess there may be a math law to explain this phenomena, could anybody show me the law or something like that?

The distribution result is : distribution

L.Maple
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  • What does "the distribution of numbers 0-9 of 2^4000" mean? – Greg Martin Mar 18 '19 at 03:28
  • @GregMartin it means distribution of the digits 0-9 in the base 10 representation of 2^4000, where the distribution of 0 is <number of occurrences of 0>/<log 2^4000>, etc... – Fomalhaut Mar 18 '19 at 03:31
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    Ok; you might use "digits" instead of "numbers" to clarify that. I think very little is known about the distribution of digits in large numbers like that; we have no reason to think that there should be any unevenness of distribution (as you observed), but proofs are hard to come by. – Greg Martin Mar 18 '19 at 04:48

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