# Spiral of Primes

Spiral of Primes

The natural numbers are arranged along an Archimedean spiral so that the squares 1, 4, 9, … are on the axis, with the primes drawn in blue, up to a circle of radius . The spiral is parametrized in polar coordinates by , . Also shown is the curve given by , (red), and its intersections with the spiral (purple boxes).

x

R

r=

n

θ=

n

r=

a+bn+c

2

n

θ=r-n

a