Variation of the Sacks Spiral (prime numbers)

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?

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.

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?

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