The real question is whether or not pi is "normal". Normality can be defined as follows:
A real number x is normal in base b if in its representation in base b all digits occur, in an asymptotic sense, equally often. In addition, for each m, the b^m different m-strings must occur equally often. In other words, lim n->inf N(s,n)/n = b^-m for each m-string s, where N(s,n) is the number of occurrences of s in the first n base-b digits of x. A number that is normal in all bases is called normal.
So far, the normality of pi has not been proven.
note: Of course there are other definitions of "random"; -- and "normal" does not always imply "random". In fact by some definitions of "random", pi is automatically disqualified because it is recursive.
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The real question is whether or not pi is "normal". Normality can be defined as follows: A real number x is normal in base b if in its representation in base b all digits occur, in an asymptotic sense, equally often. In addition, for each m, the b^m different m-strings must occur equally often. In other words, lim n->inf N(s,n)/n = b^-m for each m-string s, where N(s,n) is the number of occurrences of s in the first n base-b digits of x. A number that is normal in all bases is called normal. So far, the normality of pi has not been proven. note: Of course there are other definitions of "random"; -- and "normal" does not always imply "random". In fact by some definitions of "random", pi is automatically disqualified because it is recursive.