Composites from prime steps

Composites are sums of prime stepsThe torus, cut open. Every integer n sits at (log₂ n, depth Ω(n)). A prime is one step of (log₂ p, 1); a composite is where a chain of steps lands. Reorder the steps (dashed) and you land on the same point.
p = 2
p = 3
p = 5
p = 7
p = 11
p = 13
p ≥ 17
other composite

      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)

      depth 3.5: the pinch. φ is erased here (0)

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Choose n (2 to 128)
        
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          steplands onlog₂ ndepth
        
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The same route on the torus

        0
        
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Center: the horn torus pinches shut at depth 3.5. Every helix (faint lines) crosses it whatever its φ, and no integer lands there.