How to detect repeating random numbers?
does not yet seem to be a duplicate on this very site:
cycle detection, see also where hares catch up with turtles
(would-be comment: the question first states repetition every N iterations, next every N bytes.)
(If it didn't carry over: for each PRNG to check, have a clone. For each change in state of the original one, trigger two in the clone. If the states get identical, you detected a cycle. No deterministic PRNG with limited state can avoid it. The states need not be as small as the results; they rarely are, nowadays, and the cycle lengths are huge.)