Polar Shell Renderer prime numerators of the triangular-fractional grid  a(n,k) = n−1 + k/n

Each reduced fraction sits at radius √n, angle 2πk/n, colored by its shell s = n/gcd(k,n). Cells with a prime numerator carry a gold ring — they are the subject. The picture is not a new prime law: each shell unfolds into arithmetic progressions mod s², and the observed density follows the prime-in-progressions baseline after size correction. Click any cell to read its formula ladder; use the toggle below to turn the dragon into a housecat.

prime numerator color = shell s (dark = small s)

Cell inspector — the formula ladder

hover or click a cell to trace
(n,k) → s → Rs → prime?
shell-level comparison — current selection
select a cell to populate
Naming. This is the polar shell renderer (radius √n, angle 2πk/n), a distinct object from the one-turn square-spiral coordinatization of the radial companion paper. Same grid, different radial map.   Scope. A 2D object viewed flat; no 3D construction is claimed. Live recompute runs to N = 220; the settled result holds through N = 2000 (see the paper's N-scaling table).