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
42
73(-4,-4)4
(-4,-3)(-11

2
,-9

2
)(-9

2
,-11

2
)(-3,-4)
3
52
251(-2,8)4
(-2,7)(-4,9)(-3,10)(-1,8)
4
62
331(-9,3)4
(-9,2)(-21

2
,7

2
)(-9,5)(-15

2
,7

2
)
9

2
62
353(1,-9)4
(0,-9)(1,-10)(2,-9)(1,-8)
2
42
467(7,11)4
(8,11)(13

2
,19

2
)(5,11)(13

2
,25

2
)
9

2
62
479(-5,11)4
(-6,11)(-4,9)(-3,10)(-5,12)
4
62
701(-13,-11)4
(-14,-11)(-13,-12)(-12,-11)(-13,-10)
2
42
709(-7,-13)4
(-6,-13)(-15

2
,-29

2
)(-9,-13)(-15

2
,-23

2
)
9

2
62
751(14,8)4
(25

2
,15

2
)(15,10)(16,9)(27

2
,13

2
)
5
72
761(10,14)4
(17

2
,27

2
)(21

2
,31

2
)(23

2
,29

2
)(19

2
,25

2
)
4
62
941(-5,-15)4
(-5,-14)(-13

2
,-31

2
)(-11

2
,-33

2
)(-4,-15)
3
52
1151(-11,17)4
(-12,17)(-11,16)(-10,17)(-11,18)
2
42
1451(-19,13)4
(-20,13)(-19,12)(-18,13)(-19,14)
2
42
1759(-15,21)4
(-16,21)(-29

2
,39

2
)(-25

2
,43

2
)(-14,23)
6
72
1777(-21,9)4
(-22,9)(-21,8)(-39

2
,19

2
)(-41

2
,21

2
)
3
52
1801(-21,-15)4
(-23,-16)(-20,-13)(-19,-14)(-22,-17)
6
82
1811(-17,-21)4
(-31

2
,-41

2
)(-18,-23)(-39

2
,-43

2
)(-17,-19)
15

2
82
1949(-22,10)4
(-23,10)(-22,9)(-41

2
,21

2
)(-43

2
,23

2
)
3
52
2393(16,-24)4
(16,-25)(29

2
,-47

2
)(31

2
,-45

2
)(17,-24)
3
52
2617(26,-10)4
(49

2
,-21

2
)(27,-8)(57

2
,-19

2
)(26,-12)
15

2
82
2819(27,-17)4
(51

2
,-33

2
)(55

2
,-37

2
)(57

2
,-35

2
)(53

2
,-31

2
)
4
62
3323(13,29)4
(13,30)(23

2
,57

2
)(27

2
,53

2
)(15,28)
6
72
3347(-11,29)4
(-12,29)(-11,28)(-10,29)(-11,30)
2
42
3607(-30,24)4
(-31,24)(-30,23)(-28,25)(-29,26)
4
62
3643(-30,-12)4
(-30,-13)(-63

2
,-23

2
)(-59

2
,-19

2
)(-28,-11)
6
72
3671(-20,-30)4
(-20,-31)(-23,-28)(-22,-27)(-19,-30)
6
82
3701(10,-30)4
(9,-30)(12,-33)(13,-32)(10,-29)
6
82
3739(31,-13)4
(31,-12)(29,-14)(61

2
,-31

2
)(65

2
,-27

2
)
6
72
4073(-8,32)4
(-8,31)(-10,33)(-17

2
,69

2
)(-13

2
,65

2
)
6
72
4283(33,25)4
(33,26)(31,24)(32,23)(34,25)
4
62
4463(7,-33)4
(11

2
,-65

2
)(8,-35)(9,-34)(13

2
,-63

2
)
5
72
4691(-34,-32)4
(-35,-32)(-34,-33)(-33,-32)(-34,-31)
2
42
5227(-36,-6)4
(-37,-6)(-36,-7)(-69

2
,-11

2
)(-71

2
,-9

2
)
3
52
5297(4,-36)4
(3,-36)(9

2
,-75

2
)(11

2
,-73

2
)(4,-35)
3
52
6367(-6,40)4
(-7,40)(-11

2
,77

2
)(-9

2
,79

2
)(-6,41)
3
52
6653(31,41)4
(32,41)(30,39)(28,41)(30,43)
8
82
6659(25,41)4
(24,41)(26,39)(28,41)(26,43)
8
82
6829(-19,-41)4
(-20,-42)(-20,-39)(-17,-39)(-17,-42)
9
12
6911(42,-20)4
(42,-21)(81

2
,-39

2
)(85

2
,-35

2
)(44,-19)
6
72
7297(43,29)4
(42,29)(87

2
,55

2
)(89

2
,57

2
)(43,30)
3
52
7873(-4,-44)4
(-4,-45)(-11

2
,-87

2
)(-9

2
,-85

2
)(-3,-44)
3
52
8539(-46,-28)4
(-47,-27)(-47,-30)(-45,-30)(-45,-27)
6
10
8581(-22,-46)4
(-24,-46)(-22,-48)(-39

2
,-91

2
)(-43

2
,-87

2
)
10
92
8747(43,47)4
(42,47)(87

2
,91

2
)(45,47)(87

2
,97

2
)
9

2
62
9281(-48,-16)4
(-49,-17)(-49,-14)(-47,-14)(-47,-17)
6
10
9739(-13,-49)4
(-12,-49)(-14,-51)(-31

2
,-99

2
)(-27

2
,-95

2
)
6
72
9871(50,20)4
(50,21)(97

2
,39

2
)(99

2
,37

2
)(51,20)
3
52
9883(50,32)4
(97

2
,63

2
)(51,34)(105

2
,65

2
)(50,30)
15

2
82
9941(10,50)4
(21

2
,97

2
)(8,51)(9,52)(23

2
,99

2
)
5
72