- Experiment. Math.
- Volume 21, Issue 4 (2012), 375-384.
An Empirical Approach to the Normality of π
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.
Experiment. Math., Volume 21, Issue 4 (2012), 375-384.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63] 65-05: Experimental papers 68Q30: Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]
Bailey, David H.; Borwein, Jonathan M.; Calude, Cristian S.; Dinneen, Michael J.; Dumitrescu, Monica; Yee, Alex. An Empirical Approach to the Normality of π. Experiment. Math. 21 (2012), no. 4, 375--384. https://projecteuclid.org/euclid.em/1356038820