This is an ill formed problem. If all you need to do is pick one random number, just pick one: 0 or 1. That will be to any level of proof just as random as an

This is an ill formed problem. If all you need to do is pick one random number, just pick one: 0 or 1. That will be to any level of proof just as random as any natural method one could devise for a single number. If instead the question is about generating a series of digits, and making an argument about the randomness of thosee digits, that is a completely different problem, and one that needs more specification about how much random data is needed and what context against which that randomness will be evaluated.