# Voronoi Diagrams of the Ulam Prime Spiral

The table below shows the primes that have 'less round' Voronoi cells than any smaller prime. I conjecture that this sequence is an infinite sequence - that is, there's no 'least round' voronoi cell. If you aren't sure what all this means, check out the explanation on the main page on this topic.

p"Centre"#VerticesVertex ListAreaPerimeter(P/2)2/A
2(1,0)5
 ( 32 , 12 ) , ( 32 , - 32 ) , ( 16 , - 56 ) , ( - 14 , 0 ) , ( 0 , 12 )
 6124
 72 + 43 �5
4.132018689726583
11(2,0)5
 ( 32 , 12 ) , ( 32 , - 32 ) , ( 3 , - 2 ) , ( 3 , 0 ) , ( 2 , 1 )
 72
 4 + 32 �2 + 12 �10
4.237705522975003
23(0,-2)4
 ( 16 , - 56 ) , ( - 32 , - 52 ) , ( - 1 , - 4 ) , ( 32 , - 32 )
 256
 256 �2 + 23 �5 + 12 �10
4.821635921280641
31(3,3)4
 ( 2 , 3 ) , ( 3 , 2 ) , ( 4 , 2 ) , ( 4 , 5 )
 72
 4 + 3 �2
4.852937535496735
47(1,-3)4
 ( - 1 , - 4 ) , ( 32 , - 32 ) , ( 3 , - 2 ) , ( 12 , - 92 )
 5
 5 �2 + �10
5.236067977499791
181(7,5)4
 ( 7 , 4 ) , ( 143 , 193 ) , ( 6 , 7 ) , ( 9 , 4 )
 163
 2 + 163 �2 + 23 �5
5.706147946283363
229(8,-4)4
 ( 6 , - 5 ) , ( 9 , - 2 ) , ( 9 , - 4 ) , ( 8 , - 5 )
 4
 4 + 4 �2
5.82842712474619
1669(8,-20)3
 ( 7 , - 21 ) , ( 7 , - 18 ) , ( 10 , - 21 )
 92
 6 + 3 �2
5.828427124746191
2153(-23,-13)5
 ( - 24 , - 13 ) , ( - 24 , - 15 ) , ( - 623 , - 353 ) , ( - 1678 , - 858 ) , ( - 22 , - 11 )
 14324
 2 + 163 �2 + 38 �10 + 524 �26
5.832955450142133
4603(-12,34)6
 ( - 14 , 35 ) , ( - 11 , 32 ) , ( - 10 , 33 ) , ( - 14 , 37 ) , ( - 433 , 37 ) , ( - 292 , 732 )
 9112
 13 + 8 �2 + 23 �10
6.2375692795404465
5861(-30,-38)4
 ( - 32 , - 39 ) , ( - 28 , - 35 ) , ( - 833 , - 1103 ) , ( - 30 , - 39 )
 193
 2 + 193 �2 + 13 �26
6.32302992683966