Experimental Mathematics

An Empirical Approach to the Normality of π

David H. Bailey, Jonathan M. Borwein, Cristian S. Calude, Michael J. Dinneen, Monica Dumitrescu, and Alex Yee

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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.

Article information

Experiment. Math., Volume 21, Issue 4 (2012), 375-384.

First available in Project Euclid: 20 December 2012

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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]

Normal real normal string $\pi$ Poisson process


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

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