"The digits of pi are conjectured to be "random" in the sense of being both uniformly distributed over {0, ..., 9} and possessing no n-ary serial correlations f

"The digits of pi are conjectured to be "random" in the sense of being both uniformly distributed over {0, ..., 9} and possessing no n-ary serial correlations for any n, but as far as I know, this has not been proven." This is why I find the concept interesting. I want to see the conjectures and theories /in person./ I love mathematical theory, in general, but my knowledge is very shallow. I more-or-less understand the properties of pi that you described, but I want to test them. I also want to test the properties of Benford's law to see how they work and how they can or can't be applied. This looks like the perfect opportunity to do exactly that.