How Normal Is the MRB Constant?

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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.