In MRB constant rational?A I mentioned that normality and rationality are related in that a rational number is never normal, yet SOME irrational numbers are NOT normal. I understand that normality is harder to prove than rationality; however, we should look at normality as close as we can for clues about irrationality -- I think.
An absolutely normal number is normal in all bases; we don’t know, but the first several digits of Pi look like they could be absolutely normal in so much that they are normally distributed.
Here is an updated Demo that compares the first several digits of the MRB constant (MRB) to Pi as far as normality, in several bases, is concerned.
From my analysis so far it looks like the first several digits of MRB are more normally distributed in bases 8, 9 and 10 than the same first digits of Pi.
Remember, however, no one has proven that MRB is irrational, which it would have to be in order to be normal.