Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

An Interesting Pattern in the Prime Numbers: Parallax Compression

novaspivack.com

Post reply on HN
Print view View original

111–120 of 195 posts

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

#111

Post by airesearcher »

airesearcher wrote: post #106
mathythrowaway wrote: post #71

Earlier quoted context omitted.

But that does produce a picture identical to theirs. Because they are using 75 numbers per square, they do end up hitting at least one prime in each box with (n,k)=1 for the first 75 rows. This pattern won't continue much longer, which is why they've conveniently stopped the picture at that point.

From what we have seen in our tests, the pattern holds for the number of rows n, where n = the number of integers contained in a cell. After n rows the symmetry breaks. We haven't tested every possible n yet however. It would be great to do more tests and let's see if there are exceptions.

Actually someone did point out an exception and it generates something very interesting we didn't see before. The pattern is different for odd n. But also has an interesting self-similarity. See the discussion on Telegram about this. https://t.me/joinchat/G8AnchIna2q8yn1lGHirkA

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

#112

Post by andrepd »

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…

As far as I could gather from one of the links in the article, the definition seems to be "cell n is black if there is a prime in the interval [Rn , R(n+1)[, for R a natural number". The "pattern" supposedly holds for R rows when displayed in a triangular arrangement, equivalently R^2/2 cells

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

#113

Post by andrepd »

phyzome wrote: post #14

My gut sense is that this has something to do with visualizing the sieve of Eratosthenes, and nothing more than that. But I'd be happy to hear otherwise.

I don't intent to be rude, but what does that even mean? Can you explain?

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

#116

Post by Recursing »

andrepd wrote: post #112
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…

As far as I could gather from one of the links in the article, the definition seems to be "cell n is black if there is a prime in the interval [Rn , R(n+1)[, for R a natural number". The "pattern" supposedly holds for R rows when displayed in a triangular arrangement, equivalently R^2/2 cells

That's what they say, but the generated image is different (e.g. the first cell of the second row should be red)

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

#117

Post by shaunxcode »

anderskaseorg wrote: post #82
_rpd wrote: post #73

Earlier quoted context omitted.

The claim is that using N numbers per square will result in the pattern holding for N rows, for arbitrarily large N.

Even if I’m misunderstanding how this is supposed to work for odd n, this claim fails for plenty of even n. n = 14: fails on row 13, col 3 n = 20: fails on row 17, col 8 n = 30: fails on row 17, col 7 n = 38: fails on row 37, col 8 n = 44: fails on row 31, col 2 n = 50: fails on row 43, col 13 …

Ok going back to the mathematica version that does it the slower primality testing per terms in cell way I am seeing the deviations meaning the gcd triangle is not an exact match to what we have here.

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

#118

Post by blurbleblurble »

sixstringtheory wrote: post #110
evancox100 wrote: post #77

What would it look like if instead of a binary coloring, you used a gradient coloring representing the number of primes in each range?

I played around with the cool demo posted by no_gravity: https://news.ycombinator.com/item?id=17104652 replace the source with the one I dropped here and hit Go: https://pastebin.com/aw9nRmeZ It's actually fun to run the original first and then watch the colors overlay on top of it.

Thank you! I tried doing this with the observablehq version and got really "lost in the Ulam Spiral" of opening and closing functions.

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

#119

Post by laurilove »

Appropriate juncture to repost this: https://www.youtube.com/watch?v=sD0NjbwqlYw

"Visualizing the Riemann zeta function and analytic continuation"

(Watch the last 30s or so if nothing else. You'll not regret it.)

There is a kind of 'real' Ural spiral [or really a kind of chaotically decaying 'orbit'] related dynamic that gives the prime numbers (assuming the RH.)

Conceivable that OP's pattern might have some relation to this dynamic, and fun pondering to boot.

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

#120

Post by shaunxcode »

Recursing wrote: post #91
_rpd wrote: post #90

Earlier quoted context omitted.

Those are some pretty basic checks to miss. Perhaps I've misread OP's claim.

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.
Post reply on HN