How Normal Is the MRB Constant?

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Move the slider to compute digital expansions, in various bases , of the constant and to digits. The two rows of integers under the row of digits are the frequencies of the digits in the base expansions of and . The two rows of decimal numbers are for and .


Normality can be measured by how close the are to , say with the function . The closer is to zero, the closer is to being normal in base 10. However, any such numerical evidence is far from a proof.


Contributed by: Marvin Ray Burns (March 2011)
Open content licensed under CC BY-NC-SA



According to Wolfram MathWorld, "A normal number is an irrational number for which any finite pattern of numbers occurs with the expected limiting frequency in the expansion in a given base (or all bases). For example, for a normal decimal number, each digit 0–9 would be expected to occur 1/10 of the time."

We do not know if the MRB constant is irrational; this Demonstration looks at how normal its first 5000 digits appear to be. For comparison, we also consider the digits of ; its first 30 million digits are very uniformly distributed.

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