"there's no connection between spirals and prime numbers" You just shot yourself in the foot :( Yes, there is a connection. If you add up the total distance

"there's no connection between spirals and prime numbers" You just shot yourself in the foot :( Yes, there is a connection. If you add up the total distance each line makes in a tick, its equivalent to the harmonic series, which is a special case of the zeta function. This is where the spiral comes from. Its a dirct consequence of the fact that each number has period 1/n. The spiral emerges naturally, its not programmed or forced into that shape.