1 Introduction Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center. The trick is to arrange the spiral so all the perfect squares (1, 4, 9, 16, etc.) line up in a row on the right side:  

Figure 1

....snip...  The primes seem to cluster along certain curves. Let's zoom out even further to get a better look. The following number spiral shows all the primes that occur within the first 46,656 non-negative integers. (For clarity, non-primes have been omitted from the illustration):  

Figure 5