You can disprove randomness (by prediction) but you can't prove randomness. You can prove that certain results are as one would expect for a random source, but

You can disprove randomness (by prediction) but you can't prove randomness. You can prove that certain results are as one would expect for a random source, but that is neither guaranteed to be passed by uniform randomness, nor does passing guarantee true randomness. On a more philosophical level, as you get better measurements, entropy of a random source will always decrease. Time-stamp seeding, for example, can be weakened by timing. What can be done, on the theoretical level for PRNGs is to see how easy it is to predict the next iteration from the current iteration. An easy bound here is simply the period of the PRNG.