[gbh444g]

Are there large Ulam spirals? e.g. 100k x 100k, where each pixel is the density of prime numbers there. Do they show any interesting structure?

[zamadatix]

Sure, largely similar patterns just more zoomed out. There are well known ways to generate a coordinate conversion e.g. from http://www.survo.fi/demos/index.html#ex51

  x(n)=x(n-1)+sin(mod(int(sqrt(4*(n-2)+1)),4)*pi/2)
  y(n)=y(n-1)-cos(mod(int(sqrt(4*(n-2)+1)),4)*pi/2)

Which can make something like generating enormous spirals very quick with a simple GPU shader.