This made me curious, so I wrote a javascript version that renders a larger image of it: http://www.gibney.de/parallax_primes
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An Interesting Pattern in the Prime Numbers: Parallax Compression
121–130 of 195 posts
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#122Yep - 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!
It will be interesting to see if this pattern falls apart when the numbers are reasonably large (like roughly 300 digits+).
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#123Does this get us closer to being able to generate the Nth prime without factorization / primality test of every number?
No, very far from it
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#124From a cryptography standpoint, could this hint at attack vectors for things like discrete log problems? I've only learned of the math behind that myself recently, not sure what implications having a "topographical map of the primes" could have, especially if the pattern is relf-repeating regardless of the size of the primes.
Yes, but only up to a certain point. Larger semiprimes are still a pita to get the primes out of.
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#125Earlier 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…
Nonetheless, even though it's highly embarrassing to the parties involved, with a little bit of self-deprecating humor if I was the doctor, I could tell people at parties that I, along with Newton and Leibnitz have been published on a foundational numerical integration method. ^_^
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#126Yep - 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.
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#127Earlier 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…
Nonetheless, even though it's highly embarrassing to the parties involved, with a little bit of self-deprecating humor if I was the doctor, I could tell people at parties that I, along with Newton and Leibnitz have been published on a foundational numerical integration method. ^_^
ha!
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#128The 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…
You mean 24/tau^2, right?
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#129I wrote some code to replicate this in the console, overlaying A054521 (in colors) onto their triangle (using _ and #) for any N. The output from running
./prime-triangle.py 74
https://gist.github.com/mortehu/ccca0bafc7a9caa26d6008379057...
Edit: Other than 2, 14, 20, 30, 38, 44, 50, and 74, the two patterns match perfectly for every even N up to at least 600.
Edit 2: Looks like this is related to Linnik's theorem: https://en.wikipedia.org/wiki/Linnik%27s_theorem
Re: An Interesting Pattern in the Prime Numbers: Parallax Compression
#130Maybe it is good to know that within the sequence of all prime numbers there infinitely wide gaps : take (n+1)! +2, (n+1)! +3, ..., (n+1)! + (n+1)
That is a sequence of n consecutive numbers none of which are prime.
Not sure how that would map in this triangle shape yet.