Voronoi Diagrams of the Ulam Prime Spiral


The table below shows the primes less than 10000 whose Voronoi cells have integral area. If you aren't sure what all this means, check out the explanation on the main page on this topic.














 
p"Centre"#VerticesVertex ListAreaPerimeter
47(1,-3)4
(-1,-4)(3

2
,-3

2
)(3,-2)(1

2
,-9

2
)
5
52+10
59(2,4)4
(1,3)(1,5)(4,5)(2,3)
4
6+22
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
101(-5,5)5
(-6,4)(-6,6)(-5,7)(-3,5)(-4,4)
6
4+42
127(6,0)6
(5,-4

3
)(5,4

3
)(6,5

3
)(7,4

3
)(7,-4

3
)(6,-5

3
)
6
16

3
+4

3
10
193(-3,7)6
(-2,7)(-2,6)(-3,5)(-5,7)(-5,8)(-4,9)
7
2+62
197(-7,7)5
(-9,6)(-13

2
,17

2
)(-5,8)(-5,7)(-6,6)
6
4+7

2
2+1

2
10
229(8,-4)4
(9,-2)(6,-5)(8,-5)(9,-4)
4
4+42
251(-2,8)4
(-2,7)(-4,9)(-3,10)(-1,8)
4
62
257(-8,8)5
(-13

2
,17

2
)(-9,6)(-10,7)(-19

2
,17

2
)(-8,10)
7
13

2
2+1

2
10
271(-8,-6)5
(-7,-6)(-17

2
,-15

2
)(-19

2
,-13

2
)(-10,-5)(-7,-5)
5
4+5

2
2+1

2
10
313(3,9)3
(4,11)(1,8)(4,7)
6
4+32+10
353(1,-9)4
(0,-9)(1,-10)(2,-9)(1,-8)
2
42
367(10,-4)4
(9,-4)(9,-2)(12,-5)(11,-6)
5
2+62
389(2,10)3
(1,8)(4,11)(0,11)
6
4+32+10
439(8,-10)4
(13

2
,-21

2
)(9,-8)(10,-11)(17

2
,-25

2
)
8
62+10
449(11,-3)4
(9,-2)(12,-5)(13,-2)(10,-1)
8
42+210
479(-5,11)4
(-6,11)(-4,9)(-3,10)(-5,12)
4
62
503(-11,-7)6
(-23

2
,-17

2
)(-19

2
,-13

2
)(-10,-5)(-55

4
,-25

4
)(-27

2
,-15

2
)(-13,-8)
9
5

2
2+9

4
10+1

4
26
617(4,-12)4
(3,-12)(5,-14)(5,-12)(4,-11)
3
2+42
701(-13,-11)4
(-14,-11)(-13,-12)(-12,-11)(-13,-10)
2
42
719(3,-13)6
(3

2
,-25

2
)(4,-15)(14

3
,-44

3
)(5,-14)(3,-12)(5

3
,-12)
5
4

3
+9

2
2+2

3
5+1

6
10
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
773(-2,14)5
(-5

2
,31

2
)(0,13)(-2

3
,35

3
)(-3

2
,23

2
)(-4,14)
8
13

2
2+2

3
5+1

6
26
887(-1,15)4
(-5

2
,31

2
)(0,13)(1

2
,29

2
)(-2,17)
5
52+10
941(-5,-15)4
(-5,-14)(-13

2
,-31

2
)(-11

2
,-33

2
)(-4,-15)
3
52
1021(-12,16)4
(-12,17)(-14,15)(-11,14)(-11,16)
5
2+32+10
1091(17,-15)6
(18,-15)(18,-17)(33

2
,-33

2
)(31

2
,-31

2
)(15,-14)(17,-14)
6
4+22+10
1151(-11,17)4
(-12,17)(-11,16)(-10,17)(-11,18)
2
42
1223(15,-17)5
(31

2
,-31

2
)(38

3
,-55

3
)(77

6
,-115

6
)(41

3
,-58

3
)(33

2
,-33

2
)
6
20

3
2+1

3
26
1229(18,-14)4
(17,-14)(18,-15)(20,-13)(18,-13)
3
2+42
1283(-4,18)3
(-6,17)(-2,17)(-5,20)
6
4+32+10
1291(-12,18)4
(-13,18)(-12,17)(-11,18)(-11,20)
3
2+42
1303(-18,12)4
(-19,12)(-18,11)(-16,13)(-18,13)
3
2+42
1399(19,11)3
(18,9)(18,13)(21,10)
6
4+32+10
1429(-3,19)4
(-5,20)(-2,17)(-2,19)(-3,20)
4
4+42
1439(-13,19)6
(-13,18)(-15,18)(-29

2
,39

2
)(-25

2
,43

2
)(-35

3
,64

3
)(-11,20)
8
2+42+2

3
5+1

2
10+1

6
26
1451(-19,13)4
(-20,13)(-19,12)(-18,13)(-19,14)
2
42
1549(20,8)5
(21,8)(39

2
,13

2
)(35

2
,17

2
)(18,9)(21,10)
7
2+42+10
1567(14,20)6
(38

3
,21)(16,21)(15,18)(43

3
,52

3
)(13,18)(12,19)
10
10

3
+5

3
2+2

3
5+5

3
10
1657(-4,-20)4
(-4,-21)(-6,-19)(-5,-18)(-2,-21)
5
2+62
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
1949(-22,10)4
(-23,10)(-22,9)(-41

2
,21

2
)(-43

2
,23

2
)
3
52
2087(7,23)3
(6,21)(6,25)(8,23)
4
4+42
2111(-17,23)4
(-18,23)(-18,25)(-16,23)(-17,22)
3
2+42
2129(-23,11)5
(-23,10)(-25,10)(-47

2
,29

2
)(-22,13)(-43

2
,23

2
)
9
2+32+210
2179(-7,-23)4
(-6,-23)(-8,-25)(-19

2
,-51

2
)(-8,-21)
7
42+210
2239(24,6)6
(23,6)(23,7)(24,8)(25,8)(25,5)(24,5)
5
6+22
2243(24,10)5
(68

3
,37

3
)(26,9)(25,8)(24,8)(65

3
,31

3
)
9
1+20

3
2+5
2371(-6,-24)4
(-8,-25)(-6,-23)(-5,-23)(-3,-25)
6
6+42
2393(16,-24)4
(16,-25)(29

2
,-47

2
)(31

2
,-45

2
)(17,-24)
3
52
2423(25,-3)5
(26,-13

3
)(26,-1)(74

3
,-1

3
)(23,-2)(24,-5)
10
10

3
+5

3
2+2

3
5+5

3
10
2593(17,-25)4
(16,-25)(16,-27)(19,-24)(17,-24)
4
4+42
2663(16,26)4
(31

2
,49

2
)(18,27)(15,28)(27

2
,53

2
)
8
62+10
2693(-14,26)4
(-25

2
,51

2
)(-16,29)(-33

2
,53

2
)(-14,24)
9
15

2
2+1

2
26
2749(-26,-18)4
(-25,-20)(-55

2
,-35

2
)(-53

2
,-33

2
)(-25,-18)
4
2+52
2801(18,-26)3
(16,-27)(19,-24)(19,-28)
6
4+32+10
2819(27,-17)4
(51

2
,-33

2
)(55

2
,-37

2
)(57

2
,-35

2
)(53

2
,-31

2
)
4
62
3259(29,-19)6
(29,-20)(27,-20)(55

2
,-37

2
)(57

2
,-35

2
)(30,-17)(30,-19)
6
4+22+10
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
3433(-19,-29)4
(-19,-30)(-22,-27)(-20,-27)(-18,-29)
5
2+62
3469(17,-29)3
(16,-31)(16,-27)(19,-28)
6
4+32+10
3539(30,28)4
(30,29)(57

2
,55

2
)(59

2
,53

2
)(32,29)
4
2+52
3541(30,30)5
(30,29)(28,31)(29,32)(31,32)(32,29)
8
4+32+10
3593(-22,30)5
(-24,31)(-21,28)(-20,29)(-85

4
,131

4
)(-45

2
,65

2
)
10
11

2
2+5

4
10+1

4
26
3607(-30,24)4
(-31,24)(-30,23)(-28,25)(-29,26)
4
62
3613(-30,18)4
(-31,16)(-31,20)(-28,19)(-29,16)
9
6+210
3617(-30,14)5
(-32,15)(-86

3
,35

3
)(-82

3
,43

3
)(-29,16)(-31,16)
11
2+62+4

3
5
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
3719(28,-30)4
(55

2
,-63

2
)(30,-29)(27,-28)(51

2
,-59

2
)
8
62+10
3739(31,-13)4
(31,-12)(29,-14)(61

2
,-31

2
)(65

2
,-27

2
)
6
72
3821(-7,31)5
(-8,31)(-8,30)(-4,30)(-5,32)(-13

2
,65

2
)
7
5+3

2
2+5+1

2
10
4027(32,26)4
(33,28)(30,25)(31,24)(33,26)
5
2+62
4057(8,32)5
(10,33)(6,33)(5,32)(6,31)(9,30)
10
4+22+210
4073(-8,32)4
(-8,31)(-10,33)(-17

2
,69

2
)(-13

2
,65

2
)
6
72
4091(-26,32)3
(-27,34)(-27,30)(-24,31)
6
4+32+10
4111(-32,18)4
(-67

2
,37

2
)(-31,16)(-31,20)(-63

2
,41

2
)
6
4+52
4283(33,25)4
(33,26)(31,24)(32,23)(34,25)
4
62
4357(-33,33)4
(-34,31)(-34,36)(-32,35)(-31,32)
10
5+5+210
4363(-33,27)5
(-34,29)(-34,25)(-67

2
,49

2
)(-31,27)(-65

2
,57

2
)
8
4+9

2
2+1

2
10
4463(7,-33)4
(11

2
,-65

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

2
,-63

2
)
5
72
4481(25,-33)4
(24,-33)(26,-35)(26,-33)(25,-32)
3
2+42
4567(24,34)6
(22,35)(25,36)(26,35)(25,32)(23,32)(21,34)
13
2+42+210
4597(-6,34)5
(-9

2
,67

2
)(-7,36)(-17

2
,69

2
)(-13

2
,65

2
)(-5,32)
8
62+10
4691(-34,-32)4
(-35,-32)(-34,-33)(-33,-32)(-34,-31)
2
42
4759(32,-34)4
(63

2
,-71

2
)(103

3
,-98

3
)(95

3
,-94

3
)(59

2
,-67

2
)
10
72+4

3
5
4787(35,-9)3
(33,-8)(36,-11)(37,-8)
6
4+32+10
4789(35,-7)3
(33,-8)(36,-5)(37,-8)
6
4+32+10
4933(-35,3)3
(-36,1)(-33,4)(-37,4)
6
4+32+10
4937(-35,-1)5
(-34,-7

3
)(-34,1

3
)(-36,1)(-116

3
,-5

3
)(-36,-3)
12
8

3
+8

3
2+4

3
5+4

3
10
4999(-7,-35)4
(-5,-36)(-9,-36)(-19

2
,-71

2
)(-15

2
,-67

2
)
6
4+52
5009(3,-35)4
(1,-36)(4,-33)(4,-35)(3,-36)
4
4+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
5309(16,-36)4
(16,-35)(14,-37)(17,-38)(18,-37)
6
52+10
5443(-3,37)4
(-4,37)(-2,35)(-2,37)(-3,38)
3
2+42
5569(-19,-37)5
(-19,-36)(-41

2
,-75

2
)(-20,-39)(-17,-39)(-17,-36)
9
8+3

2
2+1

2
10
5683(38,20)4
(39,22)(36,19)(37,18)(39,20)
5
2+62
5741(-2,38)4
(-3,38)(-3,40)(-1,38)(-2,37)
3
2+42
5743(-4,38)6
(-4,37)(-6,37)(-11

2
,77

2
)(-9

2
,79

2
)(-3,40)(-3,38)
6
4+22+10
5791(-38,24)4
(-37,22)(-163

4
,103

4
)(-153

4
,109

4
)(-37,26)
10
4+52+1

2
34
5827(-38,-12)6
(-37,-12)(-39,-14)(-159

4
,-47

4
)(-77

2
,-21

2
)(-151

4
,-41

4
)(-37,-11)
6
1+42+10
5849(-38,-34)5
(-36,-35)(-40,-35)(-81

2
,-69

2
)(-75

2
,-63

2
)(-37,-32)
9
4+42+10
5867(-24,-38)3
(-23,-36)(-26,-39)(-23,-40)
6
4+32+10
6011(35,39)7
(133

4
,155

4
)(34,41)(106

3
,125

3
)(36,41)(110

3
,39)(145

4
,151

4
)(139

4
,149

4
)
10
13

6
2+2

3
5+7

3
10
6173(-29,-39)5
(-30,-39)(-28,-41)(-82

3
,-122

3
)(-53

2
,-39)(-83

3
,-110

3
)
8
13

3
2+7

3
5
6217(15,-39)4
(13,-40)(17,-40)(17,-38)(14,-37)
9
6+210
6367(-6,40)4
(-7,40)(-11

2
,77

2
)(-9

2
,79

2
)(-6,41)
3
52
6397(-36,40)4
(-69

2
,79

2
)(-37,42)(-79

2
,79

2
)(-35,38)
10
52+210
6521(0,-40)5
(-1,-38)(2,-41)(1,-42)(-1,-42)(-2,-41)
9
2+52+10
6569(41,-33)4
(39,-32)(42,-35)(43,-34)(41,-32)
5
2+62
6607(41,5)7
(39,4)(42,7)(177

4
,19

4
)(42,1)(40,1)(39,2)(155

4
,13

4
)
20
2+25

4
2+1

4
10+1

4
26+3

4
34
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
6701(-17,41)5
(-18,41)(-18,43)(-33

2
,85

2
)(-29

2
,81

2
)(-15,38)
9
2+52+1

2
10+1

2
26
6703(-19,41)5
(-18,41)(-39

2
,79

2
)(-43

2
,83

2
)(-19,44)(-18,43)
9
2+72
6733(-41,33)5
(-40,31)(-40,34)(-83

2
,71

2
)(-43,34)(-169

4
,127

4
)
9
3+32+3

2
10
6779(-41,-13)6
(-39,-14)(-43,-14)(-130

3
,-40

3
)(-83

2
,-23

2
)(-41,-34

3
)(-159

4
,-47

4
)
8
4+11

6
2+1

3
5+4

3
10
6829(-19,-41)4
(-20,-42)(-20,-39)(-17,-39)(-17,-42)
9
12
6857(9,-41)4
(9,-40)(7,-42)(8,-43)(11,-40)
5
2+62
6869(21,-41)3
(22,-42)(18,-42)(22,-38)
8
8+42
6911(42,-20)4
(42,-21)(81

2
,-39

2
)(85

2
,-35

2
)(44,-19)
6
72
6947(42,16)4
(42,17)(40,15)(41,14)(44,17)
5
2+62
6983(32,42)4
(32,41)(30,43)(32,43)(34,41)
4
4+42
7127(-42,-28)4
(-43,-29)(-43,-26)(-41,-28)(-41,-29)
4
6+22
7177(-6,-42)6
(-15

2
,-85

2
)(-11

2
,-81

2
)(-4,-41)(-9

2
,-85

2
)(-11

2
,-87

2
)(-7,-44)
7
32+210
7237(43,-31)4
(42,-31)(42,-29)(89

2
,-63

2
)(87

2
,-65

2
)
4
2+52
7247(43,-21)6
(42,-21)(42,-67

3
)(85

2
,-45

2
)(45,-20)(134

3
,-58

3
)(44,-19)
5
4

3
+9

2
2+2

3
5+1

6
10
7297(43,29)4
(42,29)(87

2
,55

2
)(89

2
,57

2
)(43,30)
3
52
7307(43,39)6
(43,40)(41,38)(43,112

3
)(45,38)(137

3
,116

3
)(45,40)
8
2+8

3
2+2

3
5+4

3
10
7411(-43,29)5
(-44,29)(-44,26)(-42,26)(-42,29)(-43,30)
7
8+22
7607(44,-6)6
(45,-8)(42,-8)(41,-7)(42,-5)(43,-4)(46,-5)
14
3+22+5+210
7649(44,36)6
(43,34)(43,112

3
)(45,38)(45,34)(134

3
,33)(130

3
,33)
9
26

3
+4

3
10
7873(-4,-44)4
(-4,-45)(-11

2
,-87

2
)(-9

2
,-85

2
)(-3,-44)
3
52
8059(-3,45)4
(-5,44)(-2,47)(-3

2
,91

2
)(-7

2
,87

2
)
5
52+10
8111(-45,35)3
(-46,37)(-46,33)(-43,34)
6
4+32+10
8369(46,42)4
(89

2
,83

2
)(93

2
,87

2
)(48,43)(45,40)
5
52+10
8389(30,46)5
(57

2
,91

2
)(61

2
,95

2
)(31,47)(31,45)(30,44)
5
2+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
8597(-6,-46)4
(-8,-45)(-5,-48)(-5,-46)(-7,-44)
5
2+62
8599(-4,-46)4
(-5,-46)(-5,-48)(-2,-47)(-4,-45)
5
2+32+10
8609(6,-46)8
(6,-45)(8,-47)(23

3
,-143

3
)(5,-49)(4,-49)(3,-48)(10

3
,-139

3
)(4,-45)
14
3+32+7

3
5+1

3
26
8681(47,-15)4
(46,-15)(46,-13)(49,-16)(48,-17)
5
2+62
8707(47,11)4
(93

2
,17

2
)(50,12)(46,14)(87

2
,23

2
)
18
92+25
8803(-13,47)5
(-13,46)(-15,46)(-15,48)(-14,49)(-12,47)
6
4+42
8849(-47,35)5
(-48,109

3
)(-48,33)(-140

3
,97

3
)(-46,33)(-46,37)
8
22

3
+2

3
2+2

3
5+2

3
10
8861(-47,23)4
(-48,23)(-48,22)(-46,22)(-46,25)
4
6+22
9067(48,-6)4
(46,-5)(49,-8)(50,-7)(49,-4)
8
42+210
9161(8,48)4
(13

2
,97

2
)(9,46)(19

2
,95

2
)(7,50)
5
52+10
9187(-18,48)4
(-33

2
,97

2
)(-39

2
,91

2
)(-21,47)(-19,51)
12
72+25
9241(-48,24)4
(-49,24)(-48,23)(-46,25)(-48,25)
3
2+42
9257(-48,8)5
(-50,7)(-50,9)(-191

4
,39

4
)(-91

2
,15

2
)(-367

8
,45

8
)
12
2+9

4
2+17

8
10+3

8
26
9281(-48,-16)4
(-49,-17)(-49,-14)(-47,-14)(-47,-17)
6
10
9337(-24,-48)6
(-25,-46)(-26,-49)(-25,-50)(-22,-50)(-22,-48)(-24,-46)
12
6+32+10
9391(30,-48)4
(29,-48)(30,-49)(32,-49)(31,-46)
5
2+32+10
9419(49,-39)3
(51,-38)(48,-41)(47,-38)
6
4+32+10
9421(49,-37)6
(47,-38)(51,-38)(207

4
,-151

4
)(103

2
,-73

2
)(51,-36)(48,-35)
10
4+1

2
2+9

4
10+1

4
26
9613(-49,41)5
(-97

2
,85

2
)(-51,40)(-50,39)(-91

2
,81

2
)(-47,42)
10
52+210
9619(-49,35)6
(-48,33)(-48,109

3
)(-50,37)(-155

3
,106

3
)(-51,34)(-50,33)
11
16

3
+8

3
2+2

3
5+2

3
10
9739(-13,-49)4
(-12,-49)(-14,-51)(-31

2
,-99

2
)(-27

2
,-95

2
)
6
72
9769(17,-49)4
(16,-49)(16,-51)(19,-48)(18,-47)
5
2+62
9781(29,-49)4
(30,-49)(28,-51)(27,-48)(29,-48)
5
2+32+10
9857(50,6)4
(51,4)(48,7)(50,7)(51,6)
4
4+42
9871(50,20)4
(50,21)(97

2
,39

2
)(99

2
,37

2
)(51,20)
3
52
9929(22,50)4
(21,50)(21,48)(23,50)(22,51)
3
2+42
9941(10,50)4
(21

2
,97

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

2
,99

2
)
5
72