This makes no sense. Prime numbers are one dimensional scalar ... numbers, they don't have coordinates. The pattern comes from how they are translated into polar tuples, but could be done with any series!
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It appears that the plots are for (r,theta) = (p,p). I have seen the prime spiral for a couple of hundred numbers before. It is interesting that they group into clusters of 3 or 4 rays. Yes, there are several such patterns (triangles, polygons etc) for primes, polynomials etc.
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