# Voronoi Diagrams of the Ulam Prime Spiral

The table below shows the primes less than 10000 whose Voronoi cells have a perimeter which is a square root of a rational. If you aren't sure what all this means, check out the explanation on the main page on this topic.

p"Centre"#VerticesVertex ListAreaPerimeter
71(-4,-2)4
 ( - 5 , - 2 ) , ( - 4 , - 3 ) , ( - 3 , - 2 ) , ( - 4 , - 1 )
 2
 4 �2
73(-4,-4)4
 ( - 4 , - 3 ) , ( - 112 , - 92 ) , ( - 92 , - 112 ) , ( - 3 , - 4 )
 3
 5 �2
251(-2,8)4
 ( - 2 , 7 ) , ( - 4 , 9 ) , ( - 3 , 10 ) , ( - 1 , 8 )
 4
 6 �2
331(-9,3)4
 ( - 9 , 2 ) , ( - 212 , 72 ) , ( - 9 , 5 ) , ( - 152 , 72 )
 92
 6 �2
353(1,-9)4
 ( 0 , - 9 ) , ( 1 , - 10 ) , ( 2 , - 9 ) , ( 1 , - 8 )
 2
 4 �2
467(7,11)4
 ( 8 , 11 ) , ( 132 , 192 ) , ( 5 , 11 ) , ( 132 , 252 )
 92
 6 �2
479(-5,11)4
 ( - 6 , 11 ) , ( - 4 , 9 ) , ( - 3 , 10 ) , ( - 5 , 12 )
 4
 6 �2
701(-13,-11)4
 ( - 14 , - 11 ) , ( - 13 , - 12 ) , ( - 12 , - 11 ) , ( - 13 , - 10 )
 2
 4 �2
709(-7,-13)4
 ( - 6 , - 13 ) , ( - 152 , - 292 ) , ( - 9 , - 13 ) , ( - 152 , - 232 )
 92
 6 �2
751(14,8)4
 ( 252 , 152 ) , ( 15 , 10 ) , ( 16 , 9 ) , ( 272 , 132 )
 5
 7 �2
761(10,14)4
 ( 172 , 272 ) , ( 212 , 312 ) , ( 232 , 292 ) , ( 192 , 252 )
 4
 6 �2
941(-5,-15)4
 ( - 5 , - 14 ) , ( - 132 , - 312 ) , ( - 112 , - 332 ) , ( - 4 , - 15 )
 3
 5 �2
1151(-11,17)4
 ( - 12 , 17 ) , ( - 11 , 16 ) , ( - 10 , 17 ) , ( - 11 , 18 )
 2
 4 �2
1451(-19,13)4
 ( - 20 , 13 ) , ( - 19 , 12 ) , ( - 18 , 13 ) , ( - 19 , 14 )
 2
 4 �2
1759(-15,21)4
 ( - 16 , 21 ) , ( - 292 , 392 ) , ( - 252 , 432 ) , ( - 14 , 23 )
 6
 7 �2
1777(-21,9)4
 ( - 22 , 9 ) , ( - 21 , 8 ) , ( - 392 , 192 ) , ( - 412 , 212 )
 3
 5 �2
1801(-21,-15)4
 ( - 23 , - 16 ) , ( - 20 , - 13 ) , ( - 19 , - 14 ) , ( - 22 , - 17 )
 6
 8 �2
1811(-17,-21)4
 ( - 312 , - 412 ) , ( - 18 , - 23 ) , ( - 392 , - 432 ) , ( - 17 , - 19 )
 152
 8 �2
1949(-22,10)4
 ( - 23 , 10 ) , ( - 22 , 9 ) , ( - 412 , 212 ) , ( - 432 , 232 )
 3
 5 �2
2393(16,-24)4
 ( 16 , - 25 ) , ( 292 , - 472 ) , ( 312 , - 452 ) , ( 17 , - 24 )
 3
 5 �2
2617(26,-10)4
 ( 492 , - 212 ) , ( 27 , - 8 ) , ( 572 , - 192 ) , ( 26 , - 12 )
 152
 8 �2
2819(27,-17)4
 ( 512 , - 332 ) , ( 552 , - 372 ) , ( 572 , - 352 ) , ( 532 , - 312 )
 4
 6 �2
3323(13,29)4
 ( 13 , 30 ) , ( 232 , 572 ) , ( 272 , 532 ) , ( 15 , 28 )
 6
 7 �2
3347(-11,29)4
 ( - 12 , 29 ) , ( - 11 , 28 ) , ( - 10 , 29 ) , ( - 11 , 30 )
 2
 4 �2
3607(-30,24)4
 ( - 31 , 24 ) , ( - 30 , 23 ) , ( - 28 , 25 ) , ( - 29 , 26 )
 4
 6 �2
3643(-30,-12)4
 ( - 30 , - 13 ) , ( - 632 , - 232 ) , ( - 592 , - 192 ) , ( - 28 , - 11 )
 6
 7 �2
3671(-20,-30)4
 ( - 20 , - 31 ) , ( - 23 , - 28 ) , ( - 22 , - 27 ) , ( - 19 , - 30 )
 6
 8 �2
3701(10,-30)4
 ( 9 , - 30 ) , ( 12 , - 33 ) , ( 13 , - 32 ) , ( 10 , - 29 )
 6
 8 �2
3739(31,-13)4
 ( 31 , - 12 ) , ( 29 , - 14 ) , ( 612 , - 312 ) , ( 652 , - 272 )
 6
 7 �2
4073(-8,32)4
 ( - 8 , 31 ) , ( - 10 , 33 ) , ( - 172 , 692 ) , ( - 132 , 652 )
 6
 7 �2
4283(33,25)4
 ( 33 , 26 ) , ( 31 , 24 ) , ( 32 , 23 ) , ( 34 , 25 )
 4
 6 �2
4463(7,-33)4
 ( 112 , - 652 ) , ( 8 , - 35 ) , ( 9 , - 34 ) , ( 132 , - 632 )
 5
 7 �2
4691(-34,-32)4
 ( - 35 , - 32 ) , ( - 34 , - 33 ) , ( - 33 , - 32 ) , ( - 34 , - 31 )
 2
 4 �2
5227(-36,-6)4
 ( - 37 , - 6 ) , ( - 36 , - 7 ) , ( - 692 , - 112 ) , ( - 712 , - 92 )
 3
 5 �2
5297(4,-36)4
 ( 3 , - 36 ) , ( 92 , - 752 ) , ( 112 , - 732 ) , ( 4 , - 35 )
 3
 5 �2
6367(-6,40)4
 ( - 7 , 40 ) , ( - 112 , 772 ) , ( - 92 , 792 ) , ( - 6 , 41 )
 3
 5 �2
6653(31,41)4
 ( 32 , 41 ) , ( 30 , 39 ) , ( 28 , 41 ) , ( 30 , 43 )
 8
 8 �2
6659(25,41)4
 ( 24 , 41 ) , ( 26 , 39 ) , ( 28 , 41 ) , ( 26 , 43 )
 8
 8 �2
6829(-19,-41)4
 ( - 20 , - 42 ) , ( - 20 , - 39 ) , ( - 17 , - 39 ) , ( - 17 , - 42 )
 9
 12
6911(42,-20)4
 ( 42 , - 21 ) , ( 812 , - 392 ) , ( 852 , - 352 ) , ( 44 , - 19 )
 6
 7 �2
7297(43,29)4
 ( 42 , 29 ) , ( 872 , 552 ) , ( 892 , 572 ) , ( 43 , 30 )
 3
 5 �2
7873(-4,-44)4
 ( - 4 , - 45 ) , ( - 112 , - 872 ) , ( - 92 , - 852 ) , ( - 3 , - 44 )
 3
 5 �2
8539(-46,-28)4
 ( - 47 , - 27 ) , ( - 47 , - 30 ) , ( - 45 , - 30 ) , ( - 45 , - 27 )
 6
 10
8581(-22,-46)4
 ( - 24 , - 46 ) , ( - 22 , - 48 ) , ( - 392 , - 912 ) , ( - 432 , - 872 )
 10
 9 �2
8747(43,47)4
 ( 42 , 47 ) , ( 872 , 912 ) , ( 45 , 47 ) , ( 872 , 972 )
 92
 6 �2
9281(-48,-16)4
 ( - 49 , - 17 ) , ( - 49 , - 14 ) , ( - 47 , - 14 ) , ( - 47 , - 17 )
 6
 10
9739(-13,-49)4
 ( - 12 , - 49 ) , ( - 14 , - 51 ) , ( - 312 , - 992 ) , ( - 272 , - 952 )
 6
 7 �2
9871(50,20)4
 ( 50 , 21 ) , ( 972 , 392 ) , ( 992 , 372 ) , ( 51 , 20 )
 3
 5 �2
9883(50,32)4
 ( 972 , 632 ) , ( 51 , 34 ) , ( 1052 , 652 ) , ( 50 , 30 )
 152
 8 �2
9941(10,50)4
 ( 212 , 972 ) , ( 8 , 51 ) , ( 9 , 52 ) , ( 232 , 992 )
 5
 7 �2