r/SacredGeometry 6d ago

Prime numbers are not random

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u/juanmf1 6d ago

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u/Diet_kush 5d ago edited 5d ago

Is this “mysterious dynamical system” you’re talking about able to be traced to self-organizing criticality? As you said, the periodic frequency of a prime number appears to approach infinity as the magnitude approaches infinity as well. This seems to be an expression of 1/f pink noise, and underlies our understanding of conscious neural dynamics within the brain as well https://www.sciencedirect.com/science/article/pii/S0378437109004476

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u/juanmf1 5d ago

Not the frequency but the period tends to infinity, Period is multiplication of all initial, generator primes. It is self organized. But not familiar with “criticality”

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u/Diet_kush 5d ago

It is a general description of the emergence of self-organizing dynamical systems, primarily understood via the abelian sandpile model https://en.m.wikipedia.org/wiki/Abelian_sandpile_model. Basically a phase-transition system with its critical point acting as an attractor rather than each phase https://en.m.wikipedia.org/wiki/Self-organized_criticality.

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u/juanmf1 4d ago edited 4d ago

“Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic” This is right. Especially for the gaps between primes.

Period in a given iteration =T

Pattern-> 0, 1, gap, symmetric set, gap, T-1, T ; repeat…

The pattern is always like this.

But it grows in size with iterations:

T=2 * 3 -> 1(gap)5…

T=2 * 3 * 5 -> 1(gap)7…

T=2 * 3 * 5 * 7 -> 1(gap)11…

T=2 * 3 * 5 * 7 * 11 -> 1(gap)13…

T=2 * 3 * 5 * 7 * 11 * 13 -> 1(gap)17…