An Interesting Pattern in the Prime Numbers: Parallax Compression

Re:An Interesting Pattern in the Prime Numbers: Parallax Com... by mathythrowaway on Friday May 18, 2018 @03:29PM (#17104273)

This just shows the reduced residues mod n. There are n squares in the nth row from the top. Color the kth square of the nth row black if gcd(k,n)=1, color it red otherwise.

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Re:An Interesting Pattern in the Prime Numbers: Parallax Com... by chickenstrips on Friday May 18, 2018 @04:17PM (#17104628)

You're correct. The correspondence just seems to be due to some bound on the prime gap for arithmetic progressions (or perhaps something even more trivial that I'm missing). A cursory search suggests it might be a consequence of Ingham's bound. In any case, it doesn't yield much of interest.

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Re:An Interesting Pattern in the Prime Numbers: Parallax Com... by tgb on Friday May 18, 2018 @03:34PM (#17104313)

That's what the OEIS sequence they link to says. I hadn't realized that it makes such a beautiful pattern!

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Re:An Interesting Pattern in the Prime Numbers: Parallax Com... by gowld on Friday May 18, 2018 @03:47PM (#17104416)

How is that?

Isn't it plotting a prime spiral, not GCD?

Obviously prime implies gcd=1, but the "kth" square isn't "k", because it's a spiral counting up from the center.

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Re:An Interesting Pattern in the Prime Numbers: Parallax Com... by mathythrowaway on Friday May 18, 2018 @03:53PM (#17104470)

No, it isn't plotting a prime spiral. Each square in their triangle is a block of 75 numbers. Within the nth row the numbers are sorted by residue mod n.

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