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Recently wrote this python demo to show a prime explosion occurring at the origin. Each radiating line represents a prime number, with its length corresponding to the prime's value. The direction each prime takes is random, resulting in a unique pattern of primes shooting out from the origin.

Example of the first $42$ prime numbers 42

Example of the first $4200$ prime numbers 4200

Question

Apart from its beauty, is there any mathematical significance or value in visualizing primes in this manner?

vengy
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    We already know that primes get larger as they get bigger, and the arrangement and coloring is random, so no? – Randall Sep 13 '23 at 16:05
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    I doubt it. If your visualization showed the density of primes in the vicinity of each radius it might suggest the prime number theorem. – Ethan Bolker Sep 13 '23 at 16:06
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    I guess if there were huge gaps in primes you could see it in various radii gaps, but that would only be anecdotal and nothing helpful in making conjectures. – Randall Sep 13 '23 at 16:07
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    Such pictures are also used in the big bang theory to "visualize" the big bang. Nice idea with the "prime explosion" , but yet every pattern that has been discovered vanished for larger primes and I am pretty sure this is no exception. – Peter Sep 13 '23 at 16:14

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