Números Primos
The distribution of prime numbers is one of the most difficult questions in mathematics. There are ways to arrange prime numbers so that some interesting patterns emerge, but yet the actual distribution remains irrational and transcendental.
The first 10 seconds of this animation show over 13 thousands prime numbers arranged in circles of 720 slots each. Only the slots corresponding to prime numbers are filled in with black ink. The distribution is rather chaotic, although some radial lines could be seen.
The middle 10 seconds show the distributions of the cubes of the prime numbers. Every black dot is on the same circle, but its location along the circle is based on the 3-rd power of the number modulo 720. Obviously, the prime dots are grouped in several radial streams.
The final 10 seconds show the rather shocking distribution of the 12-th power of the primer numbers. It appears that except for the first three prime numbers, the 12-th power of all the rest land themselves on the same slot of each circle!
Thus, is p is a prime number greater than 5, then p^12=720n+1 for some integer n.
There is nothing magic in 720. If we choose 360 slots or even 144 we still get a similar result. For those of you, thinking about asking to see the distribution of the 13-th power ... the answer is disappointing. The 13-th power of primes are distributed quite chaotically. Sorry.
The music used in this animation is from "Nullsion" by Xelysion
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