Normality and the Digits of π

The question of whether (and why) the digits of well-known constants of mathematics are statistically random in some sense has long fascinated mathematicians. Indeed, one prime motivation in computing and analyzing digits of π is to explore the age-old question of whether and why these digits appear “random.” The first computation on ENIAC in 1949 of π to 2037 decimal places was proposed by John von Neumann to shed some light on the distribution of π (and of e) [8, pp. 277–281]. Since then, numerous computer-based statistical checks of the digits of π, for instance, so far have failed to disclose any deviation from reasonable statistical norms. See, for instance, Table 1, which presents the counts of individual hexadecimal digits among the first trillion hex digits, as obtained by Yasumasa Kanada. By contrast,