Determine existence of cycle in number stream - pattern recognition for a cycle

Question

I have tried to make a pseudo Random Number Generator and generated 10000 numbers. I want to determine whether there exists a cycle in it? With my logic, there could be a cycle of maximum length (INT_MAX)**15 - generating and testing till that value is kind of not feasible. So, is there a way to recognize with N generated numbers(sufficiently large - 10007 numbers) to estimate what length of cycle will be there?

Possibly in R?

In addition to hlovdal's answer, there's the question of uniformity. Some early PRNGs had long cycles but predictable asymmetric densities (kind of like the Universe :-) ). — Carl Witthoft, Mar 20 '14 at 11:37

score 3 · Accepted Answer · answered Mar 20 '14 at 11:31

The answer to your question is probably much more complex that you would like it to be. Testing weaknesses in PRNGs is not a simple question, and it is highly dependent on the algorithm used for the PRNG. If your PRNG is of type Linear congruential generator, then a test called spectral test can be used. For other types of PRNGs there are other tests.

The paper TestU01: A C Library for Empirical Testing of Random Number Generators discusses theory and contains software examples on how to test various types.

Determine existence of cycle in number stream - pattern recognition for a cycle

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