Can one exclude the idea of prime numbers being a projection (using a proper acceptance domain) of a higher dimensional lattice onto 1D similar to the generation of Penrose tilings (see e.g. thesis)? Unfortunately I don't find papers on this topic so maybe there are simple arguments I don't come up with.

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    $\begingroup$ You won't find a precise answer there, but you could take a look at: golem.ph.utexas.edu/category/2013/06/… and mathoverflow.net/questions/133581/… $\endgroup$ Oct 31, 2017 at 23:05
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    $\begingroup$ My understanding is that growth-rate arguments exclude most of the natural ways of doing this; it's essentially impossible to get any sort of growth rate that isn't $\Theta(n^\alpha)$ via direct projection, and I don't know of any sensible ways of getting the logarithmic term. $\endgroup$ Jun 29, 2018 at 16:54


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