Trippy: the reason I made RANDOM in all caps is because that is the term that necessitates a uniform distribution. Also, with regards to your K-40 number generator it had more merit than I originally gave it. I tweaked the idea here: ...which would work. The problem that I was having is that your proposed system 1) had no way of terminating to know when the number has been selected, and 2) had no way of choosing a digit greater than 1 (either it decayed or it did not). It was therefore confusing when you would mention waiting 6 half-lives to determine 6 decimal digits. I realize now that, the binary/decimal digit issue aside, what you MEANT was that the LENGTH of the number being chosen was pre-determined, then you use the K-40 method to generate it. If that's what you meant then you are correct that it would in fact be a uniform distribution for a given length.