The goal of this project was to proof if
a) Pi is “NORMAL”,
b) the subsequences of the decimal presetation of Pi are IID (independently and identically distributed uniform draws),
c) the decimal presentation of the number Pi is “RANDOM”.
For estimating the various test results Chi square value was calculated first and compared with the critical Chi2 value on a given significance level (typically 99,5%).
Test with suspicious Chi2 values were proofed by the number of series differing more than 1, 2 or 3 sigma from mean value.
Any counterexmaple againts a), b) or c) would be of great interest.
Unsurprisingly, not any was found.