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There might be none. But I was thinking of links between number theory and physics, and this would seem like an example that would definitely solidify that link.

Are there any known natural systems, or physical systems in general (possibly designed), that test the primality of a number directly using the laws of physics? (Barring obvious examples such as machines intricately designed with interlocking parts/electronics to do such a job)

If there are none, I would not be surprised. But I was just curious.

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I think you'd be better off asking this over at mathoverflow. Actually, I recall something like this being discussed there some time ago and there were some examples where prime numbers naturally arise in nature in certain contexts. – Marek Feb 23 '11 at 9:10
Why aren't human programmed and constructed computers considered natural? – QGR Feb 23 '11 at 9:26
@QGR - They might be natural, but their primacy tests aren't the direct result of laws of physics, but rather of well-designed interlocking parts and logic. I am more interested in the former case; I already have many examples already of the latter. – Justin L. Feb 23 '11 at 9:28
Because it not enough that group theory, various geometries, and the whole study of differential and integral mathematics links math and physics. No, we need a really good connection. Right? – dmckee Feb 23 '11 at 16:42
Related: – Qmechanic Dec 2 '12 at 15:49

There are connection between some physical system and the Riemann zeta function. Here is one of the related question at mathoverflow:

As I answered there the I recently found the article about this topic which may give you some answer: "Physics of the Riemann Hypothesis"

Using the Riemann function you can build primality (at least probabilistic) test.

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