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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

#91

Post by Recursing »

_rpd wrote: post #90
anderskaseorg wrote: post #82

Earlier quoted context omitted.

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 …

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

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

#92

Post by pcmaffey »

PurpleBoxDragon wrote: post #17

Is there are particular reasoning or meaning to each dot being 6 numbers? Is there any significant changes if you pick other numbers per dot, following the same pattern? Based on the linked explanation here: https://beta.observablehq.com/@montyxcantsin/unwinding-the-u...

Because primes exist on a base 6 numeric scale. Where all prime numbers are multiples of 1 and 5.

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

#94

Post by bustadjustme »

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 …

From OP: > Interestingly, this same pattern holds for more numbers, and for different intervals.

He's not claiming it holds for _all_ n, just for _many_ n.

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

#95

Post by SomeMathComment »

chickenstrips wrote: post #76
drdeca wrote: post #75

I am a little confused. When it says that each square corresponds to n sequential numbers, does it mean that the first square is the first n, and the second square (which is on the second row) is the first n after those, and the third square (also in the second row) has the first n after those, and so on, Or, do the regions overlap? I tried to look at the first 4 rows for n=5, but did not see the pattern depicted (ea…

For fixed n, a block (x,y) contains the numbers n/2 y^2-n/2 y + yz + x for all 0 <= z < n.

(n/2)y^2-(n/2)y + yz + x

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

#96

Post by drdeca »

chickenstrips wrote: post #76
drdeca wrote: post #75

I am a little confused. When it says that each square corresponds to n sequential numbers, does it mean that the first square is the first n, and the second square (which is on the second row) is the first n after those, and the third square (also in the second row) has the first n after those, and so on, Or, do the regions overlap? I tried to look at the first 4 rows for n=5, but did not see the pattern depicted (ea…

For fixed n, a block (x,y) contains the numbers n/2 y^2-n/2 y + yz + x for all 0 <= z < n.

Making sure I am parsing that correctly:

Is that

((n/2) * y^2) - ((n/2) * y) + (y * z) + x ? (For z ranging from 0 to n)

If so, alright, that makes more sense to me, thanks.

So, n * (y * (y-1)/2) + x + y * z ?

Edit: does HN have an escape character to deal with the asterisks?

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

#97

Post by [deleted] »

anderskaseorg wrote: post #68
mathythrowaway wrote: post #65

Earlier quoted context omitted.

Their picture is correct, but only because they are doing something more ridiculous than this. Every one of the squares in their picture represents 75 numbers, not 5 numbers.

Click on the definition of T, and you see exactly the A054521 formula. T = (n, k) => { return (GCD(n, k) == 1) ? 1 : 0; } The given code doesn’t use primes, primesSet, or isPrime at all.

[deleted]

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

#98

Post by m00n »

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 unfortunately a recurring theme with amateur mathematicians: They fail to state their basic definitions and assumptions and seem all to eager to dive right into applications, be it computer graphics, cryptography or finance.

More to the point: This picture seems from a cursory inspection to plot T(k,n) with n=row, k=column from the top left. But why is this interesting?

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

#99

Post by planteen »

cabaalis wrote: post #19
tzahola wrote: post #4

The pattern looks nice, but I would have asked some mathematicians before announcing this as something novel.

I understand what you mean, but how many great breakthroughs in history were where someone shared the foundation of an idea and then another formalized it?

I think it happens fairly often.

In the more mathematical realm in information theory, turbo codes came out of nowhere by people who were not experts in the field of FEC. Their efficiency far surpassed other methods of the time, to the point that their results in the conference paper were doubted. They didn't have any understanding at the time of why they worked well, they just published results.

Lots of physical phenomena start as simple observations that are later worked into theoretical frameworks. The photoelectric effect comes to mind.

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

#100

Post by vietjtnguyen »

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
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