 # How Normal Is the MRB Constant?

Initializing live version Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .

[more]

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.

[less]

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

## Snapshots   ## Details

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.

## Permanent Citation

Marvin Ray Burns

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send