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arXiv · 1908.08925

Normality Analysis of Current World Record Computations for Catalan's Constant and Arc Length of a Lemniscate with $a=1$

Seungmin Kim
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Abstract

Catalan's constant and the lemniscate constants have been important mathematical constants of interest to the mathematical society, yet various properties are unknown. An important property of significant mathematical constants is whether they are normal numbers. This paper evaluates the normality of decimal and hexadecimal representations of current world record computations of digits for the Catalan's constant (600,000,000,100 decimal digits and 498,289,214,317 hexadecimal digits) and the arc length of a lemniscate with $a=1$ (600,000,000,000 decimal digits and 498,289,214,234 hexadecimal digits). All analyzed frequencies are persistent to the conjecture of Catalan's constant and the arc length of a lemniscate with $a=1$ being a normal number in bases 10 and 16.

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Seungmin Kim. 2022-03-05. Normality Analysis of Current World Record Computations for Catalan's Constant and Arc Length of a Lemniscate with $a=1$. https://arxiv.org/abs/1908.08925

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