Primes are what no slide reaches

A prime step is the same vector for every number: the whole cloud slides by (log₂ p, 1) and lands on the multiples of p. Apply the slides and the composites light up. What stays white is exactly the primes.

slide ×2
slide ×3
slide ×5
slide ×7
slide ×11
unreached prime
composite not yet reached
1 2 4 8 16 32 64 128 0 1 2 3 4 5 6 7 n, spaced by log₂ n: around the hole (φ) depth Ω(n): through the tube (θ) {{t.t}}
Slides applied
{{primeLine}}
{{compLine}}
{{row.name}} {{row.val}} {{f.text}}{{f.sep}}
reached by slides: {{f.text}}{{f.sep}}
{{nbrLine}}
The slides are the multiplication steps. In every block of p consecutive integers exactly one is a multiple of p, so no slide ever reaches two neighbours, and a prime is a point that no slide reaches at all.