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 :
