An Empirical Approach to the Normality of π

Abstract

Using the results of several extremely large recent computations, we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of $\pi$. This result was used by a Poisson process model of normality of $\pi$: in this model, it is extraordinarily unlikely that $\pi$ is not asymptotically normal base 16, given the normality of its initial segment.