Voronoi Diagrams of the Ulam Prime Spiral


The table below shows the primes that have Voronoi cells with area larger than any small prime. I conjecture that this sequence is an infinite sequence - that is, there's no 'largest' 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
2(1,0)5
(3

2
,1

2
)(3

2
,-3

2
)(1

6
,-5

6
)(-1

4
,0)(0,1

2
)
61

24
7

2
+4

3
5
3(1,1)5
(0,1

2
)(3

2
,1

2
)(2,1)(1

2
,5

2
)(0,7

3
)
65

24
10

3
+22+1

6
10
5(-1,1)6
(-2,1)(-1,0)(-1

4
,0)(0,1

2
)(0,7

3
)(-1

2
,5

2
)
157

48
31

12
+5

2
2+1

4
5+1

6
10
11(2,0)5
(3

2
,1

2
)(3

2
,-3

2
)(3,-2)(3,0)(2,1)
7

2
4+3

2
2+1

2
10
23(0,-2)4
(1

6
,-5

6
)(-3

2
,-5

2
)(-1,-4)(3

2
,-3

2
)
25

6
25

6
2+2

3
5+1

2
10
37(-3,3)5
(-4,3)(-4,4)(-3,5)(-3

2
,7

2
)(-3,2)
17

4
1+52
47(1,-3)4
(-1,-4)(3

2
,-3

2
)(3,-2)(1

2
,-9

2
)
5
52+10
53(4,0)5
(3,0)(3,-2)(5,-4

3
)(5,4

3
)(9

2
,3

2
)
31

6
14

3
+3

2
2+5

6
10
79(2,-4)4
(1

2
,-9

2
)(3,-2)(15

4
,-17

4
)(2,-6)
51

8
23

4
2+3

4
10
83(5,-3)5
(6,-5)(6,-5

3
)(5,-4

3
)(3,-2)(15

4
,-17

4
)
95

12
10

3
+5

2
10
137(2,6)5
(1,5)(1,8)(4,7)(14

3
,19

3
)(4,5)
49

6
6+2

3
2+2

3
5+10
233(8,0)6
(7,-4

3
)(7,4

3
)(33

4
,7

4
)(10,0)(10,-1)(9,-2)
199

24
11

3
+11

4
2+13

12
10
311(5,9)7
(4,11)(4,7)(14

3
,19

3
)(6,7)(20

3
,9)(13

2
,19

2
)(5,11)
37

4
5+13

6
2+2

3
5+5

6
10
443(11,-9)6
(10,-11)(9,-8)(10,-7)(32

3
,-20

3
)(51

4
,-35

4
)(12,-11)
259

24
2+37

12
2+1

3
5+7

4
10
673(-9,13)5
(-11,14)(-41

4
,47

4
)(-8,11)(-47

7
,104

7
)(-7,46

3
)
311

28
173

42
10+2

21
34
881(5,15)5
(4,14)(4,17)(20

3
,55

3
)(7,18)(7,14)
67

6
10+1

3
2+4

3
5
919(-15,-3)7
(-16,-5)(-121

7
,-8

7
)(-188

11
,-9

11
)(-31

2
,-1

2
)(-53

4
,-11

4
)(-57

4
,-23

4
)(-44

3
,-17

3
)
23641

1848
9

4
2+2

3
5+16

7
10+53

132
26+5

77
34
1753(-9,21)8
(-35

4
,77

4
)(-11,20)(-35

3
,64

3
)(-19

2
,47

2
)(-9,118

5
)(-17

2
,47

2
)(-7,22)(-20

3
,64

3
)
1591

120
23

4
2+5+3

4
10+1

5
26
1993(-10,-22)6
(-8,-21)(-19

2
,-51

2
)(-89

7
,-171

7
)(-13,-24)(-13,-22)(-11,-20)
519

28
2+22+25

7
10+1

7
13
2719(-26,12)7
(-25,10)(-47

2
,29

2
)(-197

8
,119

8
)(-82

3
,43

3
)(-86

3
,35

3
)(-173

6
,65

6
)(-53

2
,17

2
)
983

48
23

6
2+4

3
5+15

8
10+17

24
26
3911(-27,-31)7
(-29,-30)(-29,-34)(-28,-104

3
)(-55

2
,-69

2
)(-24,-31)(-24,-29)(-28,-29)
83

4
10+9

2
2+1

6
10+1

3
13
6427(-40,14)6
(-39,38

3
)(-39,17)(-41,17)(-259

6
,293

18
)(-1017

23
,318

23
)(-469

11
,126

11
)
200603

9108
19

3
+383

198
10+200

253
13+145

414
58
7621(44,8)8
(42,7)(122

3
,29

3
)(127

3
,34

3
)(87

2
,23

2
)(93

2
,17

2
)(234

5
,7)(369

8
,47

8
)(177

4
,19

4
)
2941

120
31

4
2+4

3
5+3

10
26+3

5
34
8867(-47,17)6
(-224

5
,19)(-50,19)(-99

2
,33

2
)(-93

2
,27

2
)(-1017

23
,318

23
)(-259

6
,293

18
)
27668

1035
26

5
+213

46
2+1

2
26+49

90
34+145

414
58