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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

#131

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…

Your point about the deviations is taken - the gcd triangle is not an exact fit for the pattern. Working on an updated version this evening. Specifically for odd n it does not work and there are occasional asymmetries.

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

#132

Post by [deleted] »

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…

[deleted]

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

#133

Post by airesearcher »

Here is a Dropbox link to the Mathematica code. Thanks to some of the input today we have found that this pattern does not exactly match the gcd triangle - which actually makes this more interesting in a way.

https://www.dropbox.com/s/d2dfwhxdmzkp4y4/a-pattern-in-the-p...

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

#134

Post by pcmaffey »

anyfoo wrote: post #105
pcmaffey wrote: post #92

Earlier quoted context omitted.

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

... I think that statement is only true for the prime number 5. ;)

Base 6:

1,2,3,4,5,6

7,8,9,10,11,12

13,14,15,16,17,18

19,20,21,22,23,24

25,26,27,28,29,30

See a pattern? 2 & 3 are the only prime numbers that are an exception. All others are multiples of 1 and 5.

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

#135

Post by dragonwriter »

pcmaffey wrote: post #92
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.

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

What you seem to mean to claim is that primes > 3 are all congruent to either 1 or 5 modulo 6.

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

#137

Post by dragonwriter »

pcmaffey wrote: post #134
anyfoo wrote: post #105

Earlier quoted context omitted.

... I think that statement is only true for the prime number 5. ;)

Base 6: 1,2,3,4,5,6 7,8,9,10,11,12 13,14,15,16,17,18 19,20,21,22,23,24 25,26,27,28,29,30 See a pattern? 2 & 3 are the only prime numbers that are an exception. All others are multiples of 1 and 5.

> All others are multiples of 1 and 5.

Assuming you used “and” when you meant “or”, that's trivially true (and redundant) in that all numbers (irrespective of base, which has no effect on this) are integer multiples of 1.

But no primes other than 5 are integer multiples of 5, in any base.

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

#138

Post by OmIsMyShield »

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.

I fiddled with your version and changed the colours to a heatmap-like colour scheme adapted from https://stackoverflow.com/questions/12875486/what-is-the-alg...

This shows the pattern again:https://imgur.com/qR4iGJb

Further fiddling ~shows~ highlights more patterns: https://imgur.com/a/Yjln2RX

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

#139

Post by pcmaffey »

dragonwriter wrote: post #137
pcmaffey wrote: post #134

Earlier quoted context omitted.

Base 6: 1,2,3,4,5,6 7,8,9,10,11,12 13,14,15,16,17,18 19,20,21,22,23,24 25,26,27,28,29,30 See a pattern? 2 & 3 are the only prime numbers that are an exception. All others are multiples of 1 and 5.

> All others are multiples of 1 and 5. Assuming you used “and” when you meant “or”, that's trivially true (and redundant) in that all numbers (irrespective of base, which has no effect on this) are integer multiples of 1. But no primes other than 5 are integer multiples of 5, in any base.

> Senary may be considered interesting in the study of prime numbers, since all primes other than 2 and 3, when expressed in senary, have 1 or 5 as the final digit.

https://en.wikipedia.org/wiki/Senary

I expressed it poorly, but not as you state, incorrectly.

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

#140

Post by Mediterraneo10 »

Senderman wrote: post #54
md224 wrote: post #31

Awesome! It's the math enthusiast's dream to come up with something new and exciting outside of academia. Recently I discovered what I thought was an interesting chaotic map, but after posting a question about it to Math StackExchange[1] and emailing one or two professors (no response, which is understandable), my obsession waned and I gave up on trying to figure out if it had any significance. Maybe I should keep tr…

Keep going! Don't forget: There's nothing bad about no-response - People are much more likely to respond on the web and email when you're wrong. ;)

> There's nothing bad about no-response - People are much more likely to respond on the web and email when you're wrong. ;)

There certainly could be something bad about no-response. As someone in academia who gets uninformed musings or crackpot theories from laypeople in his mailbox from time to time, no-response basically means “I know you are wrong, seriously wrong (and, in many crackpot cases, probably mentally ill), but I am not going to just waste my time trying to tell you that.”

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