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Umm... yes, you should actually.

Those patterns of semicircles aren't random, of course. They correspond directly to the degree of compositeness of the chosen modulus. Compare for n = 60,61,62, for example.

The higher the totient value for n, the more circles you see, basically.




Right, so I can look at the diagram and see that 59 and 61 are prime while 60 has many divisors. I can kinda see that the density of primes decreases gradually.

But I can't see a broader pattern beyond that.

Now here I can see some patterns! https://en.wikipedia.org/wiki/Ulam_spiral




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