Normal Numbers and Pseudorandom Generators

Title: Normal Numbers and Pseudorandom Generators
Creator: Bailey, David H.; Borwein, Jonathan M.
Relation: Computational and Analytical Mathematics p. 1-18
Publisher Link: http://dx.doi.org/10.1007/978-1-4614-7621-4_1
Publisher: Springer
Resource Type: book chapter
Date: 2013
Description: For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits in the base-b expansion of α appears, in the limit, with frequency b^-m. Although almost all reals in [0, 1] are b-normal for every b, it has been rather difficult to exhibit explicit examples. No results whatsoever are known, one way or the other, for the class of “natural” mathematical constants, such as π,e,2√ and log2. In this paper, we summarize some previous normality results for a certain class of explicit reals and then show that a specific member of this class, while provably 2-normal, is provably not 6-normal. We then show that a practical and reasonably effective pseudorandom number generator can be defined based on the binary digits of this constant and conclude by sketching out some directions for further research.
Subject: normal numbers; Stoneham numbers; pseudorandom number generators
Identifier: http://hdl.handle.net/1959.13/1055834
Identifier: uon:15946
Identifier: ISBN:9781461476207
Language: eng

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