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An Interesting Pattern in the Prime Numbers: Parallax Compression

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Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#151

Post by airesearcher »

shaunxcode wrote: post #120
Recursing wrote: post #91

Earlier quoted context omitted.

I think OP is a bit confused, the post is very ambiguous and on telegram he added more info but still hasn't fully formalized what he's trying to say

OP here - really it’s just a matter of I found a cool thing and wanted others ideas/input. I never had a pretense of a proof or a formalization just a cool pattern that emerges from folding the Ulam Spiral up a certain way. I think we were over zealous in the gcd triangle being an exact correspondence now as it clearly is not for some cells.

The pattern does not exactly match GCD as it turns out - but that makes it more curious actually. Here is the Mathematica code that does work for other values.

Https://GitHub.com/shaunxcode/a-pattern-in-the-primes

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#152

Post by airesearcher »

Someone wrote: post #126
airesearcher wrote: post #15

Yep - we are not claiming to be mathematicians, we're pattern hunters... this is an open invitation to others with more expertise to chime in and help figure this out... it's possible it is a minor discovery or even not a discovery... or it could be useful or even very useful. We don't know. Please help us explore it!

”we are not claiming to be mathematicians, we're pattern hunters.” “Searching for interesting tautologies” or “Hunting for patterns” are good descriptions of what mathematicians do. Mathematicians do mathematics because they want to be sure that a) they caught a pattern and b) that it is interesting. That’s what’s being discussed here.

Actually there is a pattern. Take a look at the Mathematica code on GitHub.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#153

Post by blurbleblurble »

m00n wrote: post #98

I wonder why the authors took the time to generate an image of their pattern but refrained from giving the actual DEFINITION. This does not foster constructive discussion of any possible ideas present. As can be seen in dozens of well-meaning comments here, people waste time reversing and guestimating parameters etc. Looking at the layman letters that my institute gets on a regular basis, I can say, that this is unfo…

That's because amateur mathematicians are artists :)

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#154

Post by [deleted] »

tomsmeding wrote: post #89
szemet wrote: post #53

My take, but correct me if I'm wrong. Take the relation to the GCD triangle http://oeis.org/A054521 At GCD(n,k)!=1 all numbers are divisible by GCD(n,k) therefore contains no prime At GCD(n,k)==1 we have https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arith... - so those series contain infinitely many primes - and seems like they actually contain at least one prime in all the pixels of the first N rows (but th…

You're onto it: what you say would still need to be proven is actually not even true, see anderskaseorg's comments, e.g. https://news.ycombinator.com/item?id=17104624 . So their picture is nice, and the gcd!=1 cells are all red, but the gcd=1 cells need not be black. For odd N this fails loads of times (always?), and for even N you quickly find failing cells when you start looking for it (see linked comment).

[deleted]

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#155

Post by mar77i »

airesearcher wrote: post #15

Yep - we are not claiming to be mathematicians, we're pattern hunters... this is an open invitation to others with more expertise to chime in and help figure this out... it's possible it is a minor discovery or even not a discovery... or it could be useful or even very useful. We don't know. Please help us explore it!

These visualization techniques have something going for them. I mean, it's amazing work and with new visualizations, people will make new conclusions based thereon much more easily. Analytic continuation ad nauseum. :)

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#157

Post by shaunxcode »

anderskaseorg wrote: post #63

The drawing is incorrect. More specifically, it’s a drawing of OEIS A054521 (black if gcd(row, col) == 1, red otherwise), not of the parallax compressed primes. The two drawings do not match as claimed. The first place where they differ is row 9, column 1, which is drawn as black even though none of 217, 226, 235, 244, 253, 262 are prime. It’s clear that gcd(row, col) == 1 is a necessary condition for there to be any…

Check the observable doc now https://beta.observablehq.com/@montyxcantsin/unwinding-the-u... should be more in line with original intention.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#158

Post by infogulch »

vietjtnguyen wrote: post #100
no_gravity wrote: post #86

This made me curious, so I wrote a javascript version that renders a larger image of it: http://www.gibney.de/parallax_primes

Using your frames here's the sequence as N goes from 2 to 90 with a stride of 2: https://streamable.com/l7r96

This is what I wanted to see! Like others have said this looks like it approaches that image as N grows large.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#159

Post by mar77i »

drdeca wrote: post #78
brador wrote: post #62

Earlier quoted context omitted.

I'd like to see the triangle fractal as a starting state for Conways "Game of Life".

As displayed in the image, every other row is offset by half a square from being on a grid. Maybe if you shifted everything to the left to line it up, but

Who said you couldn't have a hexagonal lattice? Instead of 8, every field has 6 neighbors. The only problem with that really is that you have to expect the 23/3 rule to look differently on that grid. So, no standard glider.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#160

Post by vokep »

It may turn out to be a pretty small part, but history was made today :) keep it up, stuff like this is awesome! You may not be mathematicians and it may turn out this is nothing hugely new, but even so, the proof of such itself is interesting. keep up the cool work!
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