# Normal Numbers

1. Feb 24, 2005

### NateTG

This is all really hard stuff, and speculation.

Normal numbers are irrational numbers that have the property that all the digits in their decimal expression are equally distributed.
http://mathworld.wolfram.com/NormalNumber.html
An example of a normal 10-number might be:
0.123456789101112131415161718192021222324252627...

Clearly whether a number is normal can depend on the base that it is represented in, so it makes sense to refer to b-normal numbers where b is the base.

An absolutely normal number is a number that is normal in any fixed base.

If a number is $p$-normal for all primes, is it necessarily absolutely normal?
If a number is $n^i$-normal for some whole number $n$ is it absolutely normal?
If a number is $p$-normal and $q$-normal is it also $pq$-normal? What about the converse?