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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

#181

Post by enedil »

QML wrote: post #178
WaxProlix wrote: post #20

> on January 18, 2018, I found a numerical sequence that generated the exact same pattern as Shaun’s pattern Does this mean that we have a sort of bloom filter-esque test for primality? (ie, it will give you a guaranteed no in O(1) but you'll have to crunch numbers to get the yes?) If so, are there implications for things that want to know "is it prime?" quickly? Crpytography comes to mind, for instance...

If by "bloom filter-esque", you mean a probabilistic way of testing whether a number is prime or not, then the answer would yes for a majority of numbers. How? Just run Fermat's little theorem on multiple values of "a" until you feel comfortable. [1] Why a majority? There are certain exceptions such as the Carmichael numbers to which we need to use slower algorithms to verify the primality of. Note that I'm assuming…

Fast primality testing is of course important from asymmetric crypto. Without it, we couldn't generate big semiprimes.

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

#182

Post by [deleted] »

scotty79 wrote: post #148

The way the numbers are picked into the 75-number groups is responsible for pretty symmetry. If you replace condition isPrime() with simpler checks: "is not divisible by 2" "is not divisible by 2 and 3" .. "... by 2, 3 and 5" .... "... by 2,3,5,7,13,17 and 23" ... you'll get more and more complex images but still symmetrical. For me the whole thing is subtle hiding of messiness of primes into the strong, pretty, symm…

[deleted]

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

#183

Post by leereeves »

airesearcher wrote: post #172
airesearcher wrote: post #146

Earlier quoted context omitted.

The rendering was for n=74 in fact, not for n=75. The pattern does seem to recur for even numbered n values and for those we think it matches GCD (where cells contain an even number of integers, and we render for the same even number of rows). But this has not been proved yet. However when n has odd values, the pattern does not always match GCD, it turns out. This is interesting and means that it may be a less “trivi…

See this animation by Ian Rust showing how the even values of n approach the GCD pattern as the values increase: https://streamable.com/l7r96 However, for odd values of n, it does not match GCD. So it's not simply a drawing of the GCD pattern.

> the even values of n approach the GCD pattern as the values increase

Meaning that the chance of finding a prime in these sequences of N numbers approaches one, after eliminating the cases that make primes impossible (n odd and r=2 mod 4, gcd(r,c) > 1).

Is there any deeper meaning to that, or is it simply that the probability of finding a prime in any sequence of n numbers approaches one as n increases, excluding sequences in which primes are impossible?

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

#184

Post by no_gravity »

scotty79 wrote: post #148

The way the numbers are picked into the 75-number groups is responsible for pretty symmetry. If you replace condition isPrime() with simpler checks: "is not divisible by 2" "is not divisible by 2 and 3" .. "... by 2, 3 and 5" .... "... by 2,3,5,7,13,17 and 23" ... you'll get more and more complex images but still symmetrical. For me the whole thing is subtle hiding of messiness of primes into the strong, pretty, symm…

I was thinking in the same direction but could not come up with a simple test. Your idea to start with "is not divisible by 2 .. 3 .. 4 .." is great.

It's interesting, that up to 4, it's a perfect pattern:

    function isPrime(n) { return n%2 && n%3 && n%4; }
As soon as you get to 'Not divisible by 5' noise starts to appear:

    function isPrime(n) { return n%2 && n%3 && n%4 && n%5; }
This 'noise' closes some gaps between the pattern and makes it look like runes.

Would any type of noise do this?

Here is how it looks like with some random noise added:

    function isPrime(n) { return n%2 && n%3 && n%4 && (Math.random()>0.95); }
It is not as structured as the version based on primes.

As of now, I'm not sure what to make of it. Maybe there is some other type of simple 'noise' that creates something as complex and logical as the primes. Maybe not.

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

#185

Post by clarry »

Mediterraneo10 wrote: post #179
Senderman wrote: post #176

Earlier quoted context omitted.

It sounds to me like you should have a prewritten response for people who were interested enough to contact you, but who don't know where to start.

I am sceptical of the ability of laymen to even meaningfully understand the field that I am in enough to contribute their own ideas. The amount of literature that would have to be read and assimilated is vast, really achievable only for academics. My prewritten response would only be “Do at least an MA in this field, then we’ll talk”.

What is the field?

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

#186

Post by lu5t »

tathougies wrote: post #61
tzahola wrote: post #9

Earlier quoted context omitted.

Well, to some extent, yes. Otherwise you’d end up like the MD who’ve “rediscovered” numerical integration (the trapezoid method) and got it published in the journal of diabetes or whatever.

> Otherwise you’d end up like the MD who’ve “rediscovered” numerical integration (the trapezoid method) and got it published in the journal of diabetes or whatever. This was shocking because calculus is a required subject in American high schools, and this American doctor presumably went to American high school, not because the doctor didn't check in with mathematicians. Frankly, it would be equally shocking if the d…

Calculus is not a requirement to graduate high school in America. Algebra, sure.

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

#187

Post by tathougies »

lu5t wrote: post #186
tathougies wrote: post #61

Earlier quoted context omitted.

> Otherwise you’d end up like the MD who’ve “rediscovered” numerical integration (the trapezoid method) and got it published in the journal of diabetes or whatever. This was shocking because calculus is a required subject in American high schools, and this American doctor presumably went to American high school, not because the doctor didn't check in with mathematicians. Frankly, it would be equally shocking if the d…

Calculus is not a requirement to graduate high school in America. Algebra, sure.

It’s surely a general education requirement in most colleges.

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

#190

Post by airesearcher »

UPDATE - Saturday May 19

Join the Telegram group to discuss: https://t.me/joinchat/G8AnchIna2q8yn1lGHirkA

Note that Even and Odd Values of N have a very different pattern. For example try using the values 99 and 99, and then 100 and 100, in this HTML preview version:

https://htmlpreview.github.io/?https://github.com/acmegeek/p...

Here is animation of increasing even values of N approaching GCD: https://streamable.com/l7r96

CODE TO TRY:

Javascript https://beta.observablehq.com/@montyxcantsin/unwinding-the-u....

Mathematica https://github.com/shaunxcode/a-pattern-in-the-primes

Perl https://www.dropbox.com/s/z5tfub5geyuctex/prime-draw.pl?dl=0

EXPLANATION:

In short, actually there are some curious patterns in this, and they are not simply equivalent to OEIS A054521 (as we, and others, initially thought they were).

For even values of n, they can be rendered by the GCD sequence, without the primality testing. But for odd values the pattern is different and GCD doesn't describe it.

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