Bailey, David H.; Borwein, Jonathan M.; Calude, Cristian S.; Dinneen, Michael J.; Dumitrescu, Monica; Yee, Alex An empirical approach to the normality of \(\pi\). (English) Zbl 1281.11077 Exp. Math. 21, No. 4, 375-384 (2012). Summary: Using the results of several extremely large recent computations by A. J. Yee and S. Kondo [10 trillion digits of pi: a case study of summing hypergeometric series to high precision on Multicore Systems http://hdl.handle.net/2142/28348], 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. Cited in 10 Documents MSC: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 03D32 Algorithmic randomness and dimension 11A63 Radix representation; digital problems Keywords:normal real; normal string; pi; Poisson process × Cite Format Result Cite Review PDF Full Text: DOI Euclid Online Encyclopedia of Integer Sequences: Triangle read by rows: T(n,k) is the smallest m >= 0 such that floor(Pi*n^m) == k (mod n), -1 if one does not exist, k = 0..n-1. References: [1] Bailey [Bailey et al. 97] David H., Mathematics of Computation 66 (218) pp 903– (1997) · Zbl 0879.11073 · doi:10.1090/S0025-5718-97-00856-9 [2] Bailey [Bailey et al. 04] David H., Journal of Number Theory Bordeaux 16 pp 487– (2004) · Zbl 1076.11045 · doi:10.5802/jtnb.457 [3] Berggren [Berggren et al. 04] L., Pi: A Source Book, (2004) [4] Borwein [Borwein and Bailey 08] J. M., Mathematics by Experiment: Plausible Reasoning in the 21st Century, (2008) · Zbl 1163.00002 [5] Borwein [Borwein and Borwein 98] J. M., Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (1998) [6] Calude [Calude 94] C. S., Developments in Language Theory pp 113– (1994) [7] Calude [Calude 02] C. S., Information and Randomness: An Algorithmic Perspective,, 2. ed. (2002) · Zbl 1055.68058 [8] Champernowne [Champernowne 33] D. G., Journal of the London Mathematical Society 8 pp 254– (1933) · Zbl 0007.33701 · doi:10.1112/jlms/s1-8.4.254 [9] Copeland [Copeland and Erdos 46] A. H., Bulletin of the American Mathematical Society pp 52– (1946) [10] Kaneko [Kaneko 10] Hajime, Integers 10 pp 31– (2010) [11] Queffelec [Queffelec 06] Martine, Dynamics and Stochastics pp 225– (2006) [12] Ross [Ross 83] S. M., Stochastic Processes (1983) · Zbl 0555.60002 [13] Schmidt [Schmidt 60] W., Pacific Journal of Mathematics 10 pp 661– (1960) · Zbl 0093.05401 · doi:10.2140/pjm.1960.10.661 [14] Snyder [Snyder and Miller 91] D. L., Random Point Processes in Time and Space (1991) · Zbl 0744.60050 [15] Stoneham [Stoneham 73] R., Acta Arithmetica 22 pp 277– (1973) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.