
Prime Number Spiral - micah_chatt
http://www.numberspiral.com/index.html
======
Pica_soO
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.

~~~
jerf
In high school, I created the number _b_ , whose absolute value is zero. I
discovered the following additional interesting facts about it: ∅

~~~
jwmerrill
You (re)discovered dual numbers!

[https://en.m.wikipedia.org/wiki/Dual_number](https://en.m.wikipedia.org/wiki/Dual_number)

~~~
jacoblambda
Non mobile link for the lazy

[https://en.wikipedia.org/wiki/Dual_number](https://en.wikipedia.org/wiki/Dual_number)

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cypherpunks01
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
No, actually the Ulam Spiral is something else, a simpler spiral to create.
Still, I too recommend the Wikipedia page.

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therein
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)

~~~
imglorp
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__
Yes it is, it is a bit hidden on the left side on the page in a details box.

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Applejinx
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
:)

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ideonexus
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/numb...](http://ideonexus.github.io/Explorable-
Explanations/math/numbermandala/)

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/ma...](https://github.com/ideonexus/Explorable-
Explanations/tree/master/math/numbermandala)

------
joshumax
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/)

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

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christophilus
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
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
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.

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bsaul
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
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.

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EGreg
I remember reading Martin Gardner writing about this.

Has anyone found an explanation since then?

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

~~~
astrobe_
I see a fingerprint. Whose finger it is, is left as an exercise to the
dreamer.

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

~~~
jordigh
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)

------
raister
Fascinating.

