Variation of the Sacks Spiral (prime numbers)

Factual Questions
1

There is a way of highlighting the prime numbers called the Sacks Spiral

by using perfect squares as an “anchor” for the spiral.

What if you used perfect cubes or perfect fourth powers?

2

The spiral is anchored on the perfect squares because it’s a two-dimensional diagram. If you wanted to anchor on perfect cubes, you’d need to arrange your “spiral” around the origin three-dimensionally somehow, which will be much less tidy. Or alternately, if you stick with a two-dimensional spiral but anchor it on the perfect cubes anyway, you’re going to end up with a density of numbers which increases as you go out.

3

Nothing of substance to add but:

  1. that is cool! Thank you for posting
  2. figure 5 looks like the Death Star
  3. we still doing that thing we used to do for lists with only two entries?
4

Not sure how related it is but here’s a little app for generating Ulam prime spirals…