https://en.wikipedia.org/wiki/...

Is an interesting read.
May have applications of measuring the randomness of RNGs, as deviation from Viswanath's constant

The different qualities of the RNG should already be documented for the particular type or function in every standard lib. There should be no need to test it by the consumers of the RNG.

Unless you mean test for the dev of the RNG.
In this case there are many tests that you can and should make. It depends on the purpose of the RNG. For instance, cryptography has different requirements on RNG than a game where the randomness is driving particles in random wind.

Damn, I love your rants! Alway something new to learn