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Say I have designed a makeshift PRNG for my personal amusement, now I would like to see how good it is. How do I benchmark its "randomness"? Ideally, I want to know a statistics test, such that if I pass it (or get a high score) I can write up a paper to announce a new state-of-the-art PRNG to the world. Yeah I know that's unlikely, but by saying this I mean I expect a really "strict" test.

I did some searching and Wikipedia points me to TestU01, which is said to be state-of-the-art, but its latest release is in 2009, or nearly ten years ago. I suppose a lot of things have happened since then.

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There is no such test. All automated tests for examining the randomness of a PRNG have limitations. If you read some papers in the literature that propose PRNGs, you might notice that they do more than just run an automated test against their scheme.

Of course you can always write up anything at any time. For the research community to find it interesting, or for practitioners to find it useful, it will probably take more than just passing an automated test. Getting a paper to be accepted at a quality peer-reviewed conference will probably require the reviewers to find it novel and interesting. For your PRNG to be adopted in practice, your PRNG will probably need to be better than existing ones in some relevant respect (perhaps it is faster and the quality of the pseudorandomness is "as good" in some sense as existing schemes; or better in some other way that implementors care about).

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