[HN Gopher] The Prime Hexagon
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The Prime Hexagon
Author : aww_dang
Score : 31 points
Date : 2021-03-05 12:43 UTC (10 hours ago)
(HTM) web link (www.hexspin.com)
(TXT) w3m dump (www.hexspin.com)
| andrewflnr wrote:
| For IMO a more meaningful phenomenon, this video by 3Blue1Brown
| explains why primes plotted as (p, p) in polar coordinates
| produce interesting patterns.
|
| https://youtu.be/EK32jo7i5LQ
| [deleted]
| pavas wrote:
| Am I missing something here?
|
| Choose any infinite sequence of binary numbers {0,1,0,0,...} and
| map the natural numbers to it. For any number not divisible by 2
| or 3, go left if it maps to 0 and right if it maps to 1.
|
| Doesn't this property still hold? That is, it's nothing to do
| with prime numbers and something to do with the quotient of
| {2,3}.
| fogof wrote:
| Yeah I think the hexagon property holds whenever you have a set
| which consists of 1 and 5 mod 6 numbers.
| AnotherGoodName wrote:
| Yep.
|
| All prime numbers above 6 are of the form 6n + 1 or 6n + 5,
| everything else is a factor of 2 or 3. If you make a choice
| that occurs on primes then no choice will be made for the 6n +
| 2/3/4 cells. This gives a well defined pattern since this is
| setup so those no choice cells are the ones that could go
| outside the bounds.
|
| You could also create a shape with 30 sides and a similar
| pattern since all primes above 30 (2 _3_ 5) are of the form 30n
| + 1, 30n + 7, 30n + 11, 30n + 13, 30n + 17, 30n + 19, 30n + 23
| or 30n + 29. Everything else is divisible by 2, 3 or 5.
|
| In fact you can do this sort of thing with any set of factors.
| There will be regular gaps in primality. Set the starting point
| so that those gaps in primality only change the direction on
| the inward sides and you'll confine all numbers within some
| larger shape.
| mkl wrote:
| > 2 _3_ 5
|
| You can avoid HN's * = italics by using spaces (2 * 3 * 5) or
| escaping the * with \ (2\\*3\\*5 gives 2*3*5).
| lupire wrote:
| 3B1B has a semi related video on how working with prime
| numbers can help you see properties that are also found in
| composite numbers, since the sequence of primes overlaps with
| many other sequences.
|
| https://m.youtube.com/watch?v=EK32jo7i5LQ
| Flocular wrote:
| The only surprising thing would be the pi-numbers. However the
| statistical evidence there isnt very strong. It's quite likely he
| looked at more than 400 series, so finding a 1 in 400-pattern in
| one of them is no surprise.
| andrewflnr wrote:
| I'm inclined to think it's boring in the opposite direction. Pi
| is everywhere. It would be more surprising if there was no link
| to pi.
| dcow wrote:
| This is from 2016. Has anything further insight been gleaned from
| this interesting property?
| bombcar wrote:
| It's been updated since then at least - there's a note that the
| sidebar doesn't work sometimes (2018).
| pstoll wrote:
| He's still working on it.
| klyrs wrote:
| Mathematically, it's not terribly deep -- at risk of being
| glib, it essentially follows from 2 and 3 being the only primes
| divisible by 2 or 3. It's pretty cool, but I wouldn't expect
| deep insights coming from this.
| gnulinux wrote:
| I don't understand why this is in HN frontpage. This is just
| numerology. There is no predictive or mathematical content here,
| right? Am I wrong?
| pstoll wrote:
| Disclaimer - friend of the author and have done the programming
| for some of his research. (Now I wish I'd cleaned it up more
| but oh well...)
|
| I'd describe him as a hobby mathematician, not formally
| trained. But I wouldn't put it in the numerology realm.
| smoldesu wrote:
| I'm pleasantly surprised, any time I see a *spin.com website I
| immediately fear for my life and grimace as I click on the link.
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