Prime spirals

Set 1, 2, 3, … out on the plane and light up only the primes. On Ulam's square spiral they crowd onto diagonals, where quadratics like 4k² + bk + c are unusually rich in primes; Sacks's spiral puts the squares on a single ray, and the primes follow curves. Wind the numbers by radians instead, n at an angle of n radians, and all the numbers fall into arms: 6 up to a few hundred, 44 up to a few thousand, 710 from the tens of thousands on, because 2π ≈ 6 ≈ 44/7 ≈ 710/113. Apart from the few small primes that divide the count, the primes sit on the arms whose index shares no factor with it: 2, 20 and 280 of them.