There might be none. But I was thinking of links between number theory and physi

Question

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.

Explanation / Answer

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

http://mathoverflow.net/questions/54501/riemann-zeta-function-connection-to-quantum-mechanics/54515#54515

As I answered there the I recently found the article about this topic which may give you some answer: "Physics of the Riemann Hypothesis" http://arxiv.org/abs/1101.3116

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

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