3 ms·

Is there are particular reasoning or meaning to each dot being 6 numbers? Is there any significant changes if you pick other numbers per dot, following the sam

Is there are particular reasoning or meaning to each dot being 6 numbers? Is there any significant changes if you pick other numbers per dot, following the same pattern? Based on the linked explanation here: https://beta.observablehq.com/@montyxcantsin/unwinding-the-ulam-spiral https://beta.observablehq.com/@montyxcantsin/unwinding-the-u...

ssewell 8y ago
I was wondering this myself. I skimmed to the code but can't find any variable for this.
_rpd 8y ago
The claim is that it is the same pattern independent of the number of integers per dot.
- ssewell 8y ago
  If the numbers of integers-per-dot was set to 1, the sequence would simply highlight prime numbers as they progress through the pyramid shape since “Parallax Compression” would no longer apply.
  - gowld 8y ago
    The triangle is a hexagon folded onto itself. That's what the "parallax" part is.
  - deleted 8y ago
    [deleted]
  - clort 8y ago
    Yet they say that this only seems valid for the number of rows equal to the number of integers-per-dot that was used. So, it would indeed highlight with reasonable certainty all the primes in the first row. (I am not a mathematician but I think that is "1" ?)
pcmaffey 8y ago
Because primes exist on a base 6 numeric scale. Where all prime numbers are multiples of 1 and 5.
- anyfoo 8y ago
  ... I think that statement is only true for the prime number 5. ;)
  - pcmaffey 8y ago
    Base 6: 1,2,3,4,5,6 7,8,9,10,11,12 13,14,15,16,17,18 19,20,21,22,23,24 25,26,27,28,29,30 See a pattern? 2 & 3 are the only prime numbers that are an exception. All others are multiples of 1 and 5.
    - dragonwriter 8y ago
      > All others are multiples of 1 and 5. Assuming you used “and” when you meant “or”, that's trivially true (and redundant) in that all numbers (irrespective of base, which has no effect on this) are integer multiples of 1. But no primes other than 5 are integer multiples of 5, in any base.
      - pcmaffey 8y ago
        > Senary may be considered interesting in the study of prime numbers, since all primes other than 2 and 3, when expressed in senary, have 1 or 5 as the final digit. https://en.wikipedia.org/wiki/Senary https://en.wikipedia.org/wiki/Senary I expressed it poorly, but not as you state, incorrectly.
        dragonwriter 8y ago
        > I expressed it poorly, but not as you state, incorrectly. No, really, it is completely incorrect to use “multiple of X in base Y” to mean “have X as the final digit in base Y” (which is equivalent to “is congruent to X modulo Y.”) 13 is not, in base 10 (or anywhere else), a multiple of 3.[0] That's just not what “multiple” means. [0] Well, the number denoted by the digits “13” in any base that is itself a multiple of 3—other than base 3 itself where “13” is not a valid number—is a multiple of 3, obviously, but we're talking about the number represented by “13” in base 10.

ssewell 8y ago

I was wondering this myself. I skimmed to the code but can't find any variable for this.

_rpd 8y ago

The claim is that it is the same pattern independent of the number of integers per dot.

ssewell 8y ago
If the numbers of integers-per-dot was set to 1, the sequence would simply highlight prime numbers as they progress through the pyramid shape since “Parallax Compression” would no longer apply.
- gowld 8y ago
  The triangle is a hexagon folded onto itself. That's what the "parallax" part is.
- deleted 8y ago
  [deleted]
- clort 8y ago
  Yet they say that this only seems valid for the number of rows equal to the number of integers-per-dot that was used. So, it would indeed highlight with reasonable certainty all the primes in the first row. (I am not a mathematician but I think that is "1" ?)

pcmaffey 8y ago

Because primes exist on a base 6 numeric scale. Where all prime numbers are multiples of 1 and 5.

anyfoo 8y ago
... I think that statement is only true for the prime number 5. ;)
- pcmaffey 8y ago
  Base 6: 1,2,3,4,5,6 7,8,9,10,11,12 13,14,15,16,17,18 19,20,21,22,23,24 25,26,27,28,29,30 See a pattern? 2 & 3 are the only prime numbers that are an exception. All others are multiples of 1 and 5.
  - dragonwriter 8y ago
    > All others are multiples of 1 and 5. Assuming you used “and” when you meant “or”, that's trivially true (and redundant) in that all numbers (irrespective of base, which has no effect on this) are integer multiples of 1. But no primes other than 5 are integer multiples of 5, in any base.
    - pcmaffey 8y ago
      > Senary may be considered interesting in the study of prime numbers, since all primes other than 2 and 3, when expressed in senary, have 1 or 5 as the final digit. https://en.wikipedia.org/wiki/Senary https://en.wikipedia.org/wiki/Senary I expressed it poorly, but not as you state, incorrectly.
      - dragonwriter 8y ago
        > I expressed it poorly, but not as you state, incorrectly. No, really, it is completely incorrect to use “multiple of X in base Y” to mean “have X as the final digit in base Y” (which is equivalent to “is congruent to X modulo Y.”) 13 is not, in base 10 (or anywhere else), a multiple of 3.[0] That's just not what “multiple” means. [0] Well, the number denoted by the digits “13” in any base that is itself a multiple of 3—other than base 3 itself where “13” is not a valid number—is a multiple of 3, obviously, but we're talking about the number represented by “13” in base 10.