7 ms·

Prime Number Spiral

193 points by micah_chatt 10y ago

raister 10y ago
Fascinating.
Applejinx 10y ago
Somewhere and someday, there is an AI which is reading this and deciding to let humanity live because we apparently can have some inkling of real beauty :)
therein 10y ago
P+41 spiral is absolutely fascinating. [1] I really want to know why they cluster there. http://www.numberspiral.com/art/14.gif http://www.numberspiral.com/art/14.gif
- stephengillie 10y ago
  It's difficult to visually diff these on mobile, but P+41 appears to mirror S-9. http://www.numberspiral.com/art/8.gif http://www.numberspiral.com/art/8.gif
- imglorp 10y ago
  There is a prime generating formula n^2 + n + 41 for n=0 to 39. Maybe this is related? http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
  - erk__ 10y ago
    Yes it is, it is a bit hidden on the left side on the page in a details box.
  - akhalr 10y ago
    This also holds for n = -1. Not much real benefit; just extends the set of n to 41 consecutive integers.
- cperciva 10y ago
  The P+41 spiral contains an unusually large number of primes because 163 is a Heegner number (https://en.wikipedia.org/wiki/Heegner_number https://en.wikipedia.org/wiki/Heegner_number).
Pica_soO 10y ago
Fascinating. And dangerous. If you see a pattern and you search a explanation for it, you can get wrapped up in the hunt and end up investing a lot of time into a wild goose chase. Our math profs warned us to do this, because if you zoom out wide enough, there is a pattern in every noise. As a undergrad, i got obsessed with the idea of creating a meaningful divide by zero operation. The result, if i remember correctly, was a "fractal" cave, interconnected, the walls defined by aggregated infinitys reseeded by the "echos" of all previous caves until the next "digit" of the original seed number is reached. What a useless operation, one might think- but i got obsessed with it, because it generated sequences. 1/0 = |1|0/0=1|2|3|5 Some of the results started to look like the fibonacci-sequence(its basically a algorithm mapped to infinity echoing back and forth along the cave-walls after all) and i lost a semester chasing this numeric day dream. :( Shame on me, i woke up when my math prof zoomed out over some random pattern revealing "patterns". The Truth is, we humans want to see patterns. Desperately. So desperatly it can eat lives. Still a fascinating read, can fully recommend. But wake up if you what you find eats you. PS: To double my shame, i did never publish this. So if you venture down the rabbit sinkhole, put a warning sign up.
- drvdevd 10y ago
  I haven't read the article yet but your comment just reminded me of one of my all-time favorite movies: Pi (1998). Please watch it if you haven't! [edit] took a look and this is quite beautiful. Of course the search for a pattern in the primes could easily take over your mind...
  - leeoniya 10y ago
    i liked Pi a lot, but the thing that nagged me is how any name that could ever hope to be spoken be represented by 216 digits :/
    - deleted 10y ago
      [deleted]
    - hvidgaard 10y ago
cypherpunks01 10y ago
Also known as the "Ulam Spiral" for Stanislaw Ulam who discovered it by accident in 1963, supposedly while doodling during a boring presentation. This page is great, but the wikipedia page is too and provides other related work and coincidences. https://en.wikipedia.org/wiki/Ulam_spiral https://en.wikipedia.org/wiki/Ulam_spiral
- Nomentatus 10y ago
  No, actually the Ulam Spiral is something else, a simpler spiral to create. Still, I too recommend the Wikipedia page.
- blazespin 10y ago
  Looks like a variant, sacks spiral? Hmm, sacks is the OP.
EGreg 10y ago
I remember reading Martin Gardner writing about this. Has anyone found an explanation since then?
Random_BSD_Geek 10y ago
Looks a little bit an ASCII-art Deathstar. I think I see where a direct hit could set off a chain reaction....
- banku_brougham 10y ago
  Awsome, yes the x-wing fighters gotta go right through the trench on the right
- astrobe_ 10y ago
  I see a fingerprint. Whose finger it is, is left as an exercise to the dreamer.
christophilus 10y ago
I wonder if those lines he mentions are anything like the ones I found in my visualization a while back: http://chrisdavies.github.io/primepattern/ http://chrisdavies.github.io/primepattern/ This never led me anywhere, for the record.
- chei0iaV 10y ago
  You get the lines because you're lining up all numbers divisible by 2, 3, 5 and 7. You get a very similar pattern with 210, and a sparser one with, for example, 30030.
  - christophilus 10y ago
    Yes, that's right. I wonder if it's a similar thing showing up in the spiral. Just a simple consequence like the one that causes the lines.
TwoBit 10y ago
How does this look with numbering in base 8 instead of 10?
- jordigh 10y ago
  The base has nothing to do with it. The "pattern" (it never looked like much of a pattern to me) arises from putting it on a grid, not from the choice of base. You can pick different sorts of grids and get different versions of "patterns": https://en.wikipedia.org/wiki/Ulam_spiral#Variants https://en.wikipedia.org/wiki/Ulam_spiral#Variants
bsaul 10y ago
since there are a few math experts here : it just occured to me that number factorization may be similar to compression ( saying 8 is 4 times two feels a bit like compressing a data by composing smaller elements). are there any theory approaching the prime number problems using tools from information theory (shannon and co) ?
- effie 10y ago
  It is a different representation of a number, but it achieves compression only for some numbers like 2^n for n>13. Primes and products where each prime factor is only once will be generally longer than ordinary notation.
jiyinyiyong 10y ago
Might be useless, but I got some pictures for primes too http://jiyinyiyong.blog.163.com/blog/static/6469987620111311312374/ http://jiyinyiyong.blog.163.com/blog/static/6469987620111311...
joshumax 10y ago
My friend discovered an interesting way to visualize prime numbers on an integer grid a while back. I whipped up a quick visualizer for it: https://codepen.io/joshumax/full/rOrBPz/ https://codepen.io/joshumax/full/rOrBPz/
ideonexus 10y ago
I enjoy exploring these patterns, not just for primes, but for factors as well. I made a little JavaScript app for creating "Number Mandellas" that my kids and I use to enjoy different patterns: http://ideonexus.github.io/Explorable-Explanations/math/numbermandala/ http://ideonexus.github.io/Explorable-Explanations/math/numb... Our favorite thing to do is set the Preset to "Randomized" and click "Render Preset" over and over again to see what comes up. Sorry for the clunky interface, but the source is on github if anyone wants it. https://github.com/ideonexus/Explorable-Explanations/tree/master/math/numbermandala https://github.com/ideonexus/Explorable-Explanations/tree/ma...

193 points by micah_chatt 10y ago

Fascinating.

Somewhere and someday, there is an AI which is reading this and deciding to let humanity live because we apparently can have some inkling of real beauty :)

therein 10y ago

P+41 spiral is absolutely fascinating. [1] I really want to know why they cluster there. http://www.numberspiral.com/art/14.gif http://www.numberspiral.com/art/14.gif

stephengillie 10y ago
It's difficult to visually diff these on mobile, but P+41 appears to mirror S-9. http://www.numberspiral.com/art/8.gif http://www.numberspiral.com/art/8.gif
imglorp 10y ago
There is a prime generating formula n^2 + n + 41 for n=0 to 39. Maybe this is related? http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
- erk__ 10y ago
  Yes it is, it is a bit hidden on the left side on the page in a details box.
- akhalr 10y ago
  This also holds for n = -1. Not much real benefit; just extends the set of n to 41 consecutive integers.
cperciva 10y ago
The P+41 spiral contains an unusually large number of primes because 163 is a Heegner number (https://en.wikipedia.org/wiki/Heegner_number https://en.wikipedia.org/wiki/Heegner_number).

Pica_soO 10y ago

Fascinating. And dangerous. If you see a pattern and you search a explanation for it, you can get wrapped up in the hunt and end up investing a lot of time into a wild goose chase. Our math profs warned us to do this, because if you zoom out wide enough, there is a pattern in every noise. As a undergrad, i got obsessed with the idea of creating a meaningful divide by zero operation. The result, if i remember correctly, was a "fractal" cave, interconnected, the walls defined by aggregated infinitys reseeded by the "echos" of all previous caves until the next "digit" of the original seed number is reached. What a useless operation, one might think- but i got obsessed with it, because it generated sequences. 1/0 = |1|0/0=1|2|3|5 Some of the results started to look like the fibonacci-sequence(its basically a algorithm mapped to infinity echoing back and forth along the cave-walls after all) and i lost a semester chasing this numeric day dream. :( Shame on me, i woke up when my math prof zoomed out over some random pattern revealing "patterns". The Truth is, we humans want to see patterns. Desperately. So desperatly it can eat lives. Still a fascinating read, can fully recommend. But wake up if you what you find eats you. PS: To double my shame, i did never publish this. So if you venture down the rabbit sinkhole, put a warning sign up.

drvdevd 10y ago
I haven't read the article yet but your comment just reminded me of one of my all-time favorite movies: Pi (1998). Please watch it if you haven't! [edit] took a look and this is quite beautiful. Of course the search for a pattern in the primes could easily take over your mind...
- leeoniya 10y ago
  i liked Pi a lot, but the thing that nagged me is how any name that could ever hope to be spoken be represented by 216 digits :/
  - deleted 10y ago
    [deleted]
  - hvidgaard 10y ago

cypherpunks01 10y ago

Also known as the "Ulam Spiral" for Stanislaw Ulam who discovered it by accident in 1963, supposedly while doodling during a boring presentation. This page is great, but the wikipedia page is too and provides other related work and coincidences. https://en.wikipedia.org/wiki/Ulam_spiral https://en.wikipedia.org/wiki/Ulam_spiral

Nomentatus 10y ago
No, actually the Ulam Spiral is something else, a simpler spiral to create. Still, I too recommend the Wikipedia page.
blazespin 10y ago
Looks like a variant, sacks spiral? Hmm, sacks is the OP.

EGreg 10y ago

I remember reading Martin Gardner writing about this. Has anyone found an explanation since then?

Random_BSD_Geek 10y ago

Looks a little bit an ASCII-art Deathstar. I think I see where a direct hit could set off a chain reaction....

banku_brougham 10y ago
Awsome, yes the x-wing fighters gotta go right through the trench on the right
astrobe_ 10y ago
I see a fingerprint. Whose finger it is, is left as an exercise to the dreamer.

christophilus 10y ago

I wonder if those lines he mentions are anything like the ones I found in my visualization a while back: http://chrisdavies.github.io/primepattern/ http://chrisdavies.github.io/primepattern/ This never led me anywhere, for the record.

chei0iaV 10y ago
You get the lines because you're lining up all numbers divisible by 2, 3, 5 and 7. You get a very similar pattern with 210, and a sparser one with, for example, 30030.
- christophilus 10y ago
  Yes, that's right. I wonder if it's a similar thing showing up in the spiral. Just a simple consequence like the one that causes the lines.

TwoBit 10y ago

How does this look with numbering in base 8 instead of 10?

jordigh 10y ago
The base has nothing to do with it. The "pattern" (it never looked like much of a pattern to me) arises from putting it on a grid, not from the choice of base. You can pick different sorts of grids and get different versions of "patterns": https://en.wikipedia.org/wiki/Ulam_spiral#Variants https://en.wikipedia.org/wiki/Ulam_spiral#Variants

bsaul 10y ago

since there are a few math experts here : it just occured to me that number factorization may be similar to compression ( saying 8 is 4 times two feels a bit like compressing a data by composing smaller elements). are there any theory approaching the prime number problems using tools from information theory (shannon and co) ?

effie 10y ago
It is a different representation of a number, but it achieves compression only for some numbers like 2^n for n>13. Primes and products where each prime factor is only once will be generally longer than ordinary notation.

jiyinyiyong 10y ago

Might be useless, but I got some pictures for primes too http://jiyinyiyong.blog.163.com/blog/static/6469987620111311312374/ http://jiyinyiyong.blog.163.com/blog/static/6469987620111311...

joshumax 10y ago

My friend discovered an interesting way to visualize prime numbers on an integer grid a while back. I whipped up a quick visualizer for it: https://codepen.io/joshumax/full/rOrBPz/ https://codepen.io/joshumax/full/rOrBPz/

ideonexus 10y ago

I enjoy exploring these patterns, not just for primes, but for factors as well. I made a little JavaScript app for creating "Number Mandellas" that my kids and I use to enjoy different patterns: http://ideonexus.github.io/Explorable-Explanations/math/numbermandala/ http://ideonexus.github.io/Explorable-Explanations/math/numb... Our favorite thing to do is set the Preset to "Randomized" and click "Render Preset" over and over again to see what comes up. Sorry for the clunky interface, but the source is on github if anyone wants it. https://github.com/ideonexus/Explorable-Explanations/tree/master/math/numbermandala https://github.com/ideonexus/Explorable-Explanations/tree/ma...