Voronoi Diagrams of the Ulam Prime Spiral


The table below shows information about the Voronoi Cells of the Ulam Prime Spiral, for all primes less than 1000. If you aren't sure what that 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
7(-1,-1)6
(-2,-1)(-2,-2)(-3

2
,-5

2
)(1

6
,-5

6
)(-1

4
,0)(-1,0)
155

48
7

4
+19

6
2+5

12
5
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
13(2,2)5
(2,1)(1

2
,5

2
)(1,3)(2,3)(3,2)
11

4
1+42
17(-2,2)5
(-3,2)(-3,1)(-2,1)(-1

2
,5

2
)(-3

2
,7

2
)
7

2
2+42
19(-2,0)5
(-2,-1)(-7

2
,1

2
)(-3,1)(-2,1)(-1,0)
11

4
1+42
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
29(3,1)5
(2,1)(3,0)(9

2
,3

2
)(4,2)(3,2)
11

4
1+42
31(3,3)4
(2,3)(3,2)(4,2)(4,5)
7

2
4+32
37(-3,3)5
(-4,3)(-4,4)(-3,5)(-3

2
,7

2
)(-3,2)
17

4
1+52
41(-3,-1)6
(-4,-1)(-4,1

3
)(-7

2
,1

2
)(-2,-1)(-2,-2)(-3,-2)
10

3
10

3
+5

2
2+1

6
10
43(-3,-3)6
(-4,-3)(-3,-4)(-1,-4)(-3

2
,-5

2
)(-2,-2)(-3,-2)
17

4
3+5

2
2+1

2
10
47(1,-3)4
(3

2
,-3

2
)(-1,-4)(1

2
,-9

2
)(3,-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
59(2,4)4
(1,3)(1,5)(4,5)(2,3)
4
6+22
61(0,4)7
(0,5)(-3

2
,7

2
)(-1

2
,5

2
)(0,7

3
)(1

2
,5

2
)(1,3)(1,5)
55

12
3+32+1

3
10
67(-4,2)8
(-5,2)(-5,1)(-9

2
,1

2
)(-4,1

3
)(-7

2
,1

2
)(-3,1)(-3,2)(-4,3)
23

6
2+32+1

3
10
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
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

3
)(6,-5)(15

4
,-17

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

3
)
95

12
10

3
+5

2
10
89(5,3)6
(4,5)(4,2)(9

2
,3

2
)(5,4

3
)(6,5

3
)(6,3)
59

12
13

3
+5

2
2+1

2
10
97(-1,5)5
(0,5)(-3

2
,7

2
)(-3,5)(-2,6)(-1,6)
17

4
1+52
101(-5,5)5
(-6,4)(-6,6)(-5,7)(-3,5)(-4,4)
6
4+42
103(-5,3)5
(-5,2)(-13

2
,7

2
)(-6,4)(-4,4)(-4,3)
13

4
3+32
107(-5,-1)5
(-9

2
,1

2
)(-7,-2)(-5,-2)(-4,-1)(-4,1

3
)
23

6
10

3
+7

2
2+1

6
10
109(-5,-3)5
(-4,-3)(-11

2
,-9

2
)(-25

4
,-17

4
)(-7,-2)(-5,-2)
19

4
2+5

2
2+10
113(-3,-5)5
(-3,-4)(-9

2
,-11

2
)(-17

4
,-25

4
)(-2,-7)(-1,-4)
27

4
2+3

2
2+210
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
131(6,4)4
(6,3)(4,5)(14

3
,19

3
)(7,4)
13

3
16

3
2+2

3
5
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
139(0,6)4
(-1,6)(0,5)(1,5)(1,8)
7

2
4+32
149(-6,2)5
(-7,1)(-7,10

3
)(-13

2
,7

2
)(-5,2)(-5,1)
23

6
16

3
+3

2
2+1

6
10
151(-6,0)5
(-9

2
,1

2
)(-7,-2)(-17

2
,-1

2
)(-7,1)(-5,1)
13

2
2+62
157(-6,-6)7
(-7,-6)(-7,-5)(-25

4
,-17

4
)(-11

2
,-9

2
)(-9

2
,-11

2
)(-17

4
,-25

4
)(-11

2
,-15

2
)
11

2
1+9

2
2+1

2
10
163(0,-6)5
(1,-7)(-2,-7)(-1,-4)(1

2
,-9

2
)(2,-6)
31

4
3+5

2
2+3

2
10
167(4,-6)4
(7

2
,-15

2
)(6,-5)(15

4
,-17

4
)(2,-6)
51

8
23

4
2+3

4
10
173(7,-3)4
(6,-5)(6,-5

3
)(7,-4

3
)(9,-2)
17

3
10

3
+32+10
179(7,3)6
(6,3)(6,5

3
)(7,4

3
)(33

4
,7

4
)(9,4)(7,4)
71

12
10

3
+2+3

2
10
181(7,5)4
(7,4)(14

3
,19

3
)(6,7)(9,4)
16

3
2+16

3
2+2

3
5
191(-1,7)5
(-2,7)(-2,6)(-1,6)(1,8)(-1,8)
7

2
4+32
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
199(-7,5)7
(-6,6)(-6,4)(-13

2
,7

2
)(-7,10

3
)(-15

2
,7

2
)(-9,5)(-9,6)
19

3
6+22+1

3
10
211(-7,-7)5
(-7,-6)(-17

2
,-15

2
)(-8,-9)(-22

3
,-28

3
)(-11

2
,-15

2
)
65

12
29

6
2+1

3
5+1

2
10
223(5,-7)5
(7

2
,-15

2
)(6,-5)(27

4
,-29

4
)(5,-9)(4,-9)
57

8
1+17

4
2+5

4
10
227(8,-6)5
(8,-5)(10,-7)(9,-8)(27

4
,-29

4
)(6,-5)
29

4
2+32+3

2
10
229(8,-4)4
(9,-2)(6,-5)(8,-5)(9,-4)
4
4+42
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
239(8,6)4
(9,4)(6,7)(9,7)(39

4
,25

4
)
45

8
3+15

4
2+3

4
10
241(8,8)5
(9,7)(6,7)(20

3
,9)(8,9)(9,8)
29

6
16

3
+2+2

3
10
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
263(-8,2)6
(-9,2)(-9,-2

5
)(-17

2
,-1

2
)(-7,1)(-7,10

3
)(-15

2
,7

2
)
341

60
71

15
+32+1

6
10+1

10
26
269(-8,-4)4
(-10,-5)(-7,-2)(-25

4
,-17

4
)(-7,-5)
45

8
3+15

4
2+3

4
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
277(-4,-8)4
(-4,-9)(-11

2
,-15

2
)(-17

4
,-25

4
)(-2,-7)
39

8
19

4
2+3

4
10
281(0,-8)5
(0,-9)(-4

3
,-9)(-2,-7)(1,-7)(1,-8)
29

6
16

3
+2+2

3
10
283(2,-8)6
(1,-8)(1,-7)(2,-6)(7

2
,-15

2
)(4,-9)(2,-9)
23

4
3+7

2
2+1

2
10
293(9,-5)5
(8,-5)(10,-7)(32

3
,-20

3
)(11,-6)(9,-4)
25

6
52+2

3
5
307(9,9)5
(8,9)(9,8)(10,9)(10,10)(19

2
,21

2
)
11

4
1+42
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
313(3,9)3
(4,11)(1,8)(4,7)
6
4+32+10
317(-1,9)6
(-1,8)(-3,10)(-3

2
,23

2
)(-2

3
,35

3
)(0,11)(1,8)
53

6
2+25

6
2+10+1

6
26
331(-9,3)4
(-9,2)(-21

2
,7

2
)(-9,5)(-15

2
,7

2
)
9

2
62
337(-9,-3)5
(-10,-5)(-10,-3

5
)(-9,-2

5
)(-17

2
,-1

2
)(-7,-2)
79

10
22

5
+9

2
2+3

10
26
347(-5,-9)5
(-4,-9)(-4,-11)(-7,-10)(-22

3
,-28

3
)(-11

2
,-15

2
)
83

12
2+10

3
2+1

3
5+10
349(-3,-9)7
(-4,-9)(-4,-11)(-7

2
,-23

2
)(-8

3
,-35

3
)(-2,-11)(-4

3
,-9)(-2,-7)
49

6
2+19

6
2+4

3
10+1

6
26
353(1,-9)4
(0,-9)(1,-10)(2,-9)(1,-8)
2
42
359(7,-9)4
(13

2
,-21

2
)(9,-8)(27

4
,-29

4
)(5,-9)
51

8
23

4
2+3

4
10
367(10,-4)4
(9,-4)(9,-2)(12,-5)(11,-6)
5
2+62
373(10,2)5
(33

4
,7

4
)(9,4)(45

4
,13

4
)(47

4
,7

4
)(10,0)
17

2
7

2
2+210
379(10,8)6
(9,8)(9,7)(39

4
,25

4
)(21

2
,13

2
)(23

2
,15

2
)(10,9)
33

8
1+17

4
2+1

4
10
383(8,10)6
(8,11)(13

2
,19

2
)(20

3
,9)(8,9)(19

2
,21

2
)(28

3
,11)
11

3
8

3
+32+1

3
10
389(2,10)3
(4,11)(1,8)(0,11)
6
4+32+10
397(-6,10)6
(-6,11)(-4,9)(-5,8)(-13

2
,17

2
)(-8,10)(-8,11)
29

4
3+9

2
2+1

2
10
401(-10,10)5
(-23

2
,21

2
)(-19

2
,17

2
)(-8,10)(-8,11)(-41

4
,47

4
)
53

8
1+19

4
2+3

4
10
409(-10,2)7
(-11,10

3
)(-11,0)(-21

2
,-1

2
)(-10,-3

5
)(-9,-2

5
)(-9,2)(-21

2
,7

2
)
101

15
86

15
+22+1

6
10+3

10
26
419(-10,-8)5
(-23

2
,-17

2
)(-19

2
,-13

2
)(-17

2
,-15

2
)(-8,-9)(-11,-9)
21

4
3+7

2
2+1

2
10
421(-10,-10)4
(-11,-9)(-11,-11)(-21

2
,-23

2
)(-8,-9)
17

4
5+32
431(0,-10)5
(1,-11)(-2,-11)(-4

3
,-9)(0,-9)(1,-10)
29

6
16

3
+2+2

3
10
433(2,-10)5
(1,-10)(1,-11)(3

2
,-23

2
)(4,-9)(2,-9)
15

4
3+42
439(8,-10)4
(13

2
,-21

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

2
,-25

2
)
8
62+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
449(11,-3)4
(9,-2)(12,-5)(13,-2)(10,-1)
8
42+210
457(11,5)6
(12,5)(12,4)(45

4
,13

4
)(9,4)(39

4
,25

4
)(21

2
,13

2
)
51

8
1+9

4
2+7

4
10
461(11,9)5
(10,9)(10,10)(12,10)(12,23

3
)(23

2
,15

2
)
23

6
16

3
+3

2
2+1

6
10
463(11,11)7
(10,10)(12,10)(27

2
,23

2
)(13,12)(29

3
,12)(28

3
,11)(19

2
,21

2
)
20

3
16

3
+5

2
2+1

2
10
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
487(-11,9)6
(-23

2
,21

2
)(-19

2
,17

2
)(-10,7)(-11,7)(-13,9)(-13,10)
15

2
2+42+10
491(-11,5)8
(-13,5)(-13,4)(-11,10

3
)(-21

2
,7

2
)(-9,5)(-9,6)(-10,7)(-11,7)
121

12
3+9

2
2+5

6
10
499(-11,-3)4
(-25

2
,-5

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

5
)(-21

2
,-1

2
)
61

10
22

5
+9

2
2+1

10
26
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
509(-9,-11)7
(-21

2
,-23

2
)(-8,-9)(-22

3
,-28

3
)(-7,-10)(-15

2
,-23

2
)(-9,-13)(-10,-13)
95

12
1+42+2

3
5+10
521(3,-11)5
(4,-9)(3

2
,-23

2
)(5

3
,-12)(3,-12)(4,-11)
23

6
10

3
+7

2
2+1

6
10
523(5,-11)5
(4,-11)(4,-9)(5,-9)(13

2
,-21

2
)(5,-12)
19

4
3+42
541(12,0)5
(13,4

3
)(13,-2)(10,-1)(10,0)(47

4
,7

4
)
191

24
13

3
+7

4
2+17

12
10
547(12,6)6
(12,5)(21

2
,13

2
)(23

2
,15

2
)(12,23

3
)(25

2
,15

2
)(27

2
,13

2
)
13

3
52+1

3
10
557(8,12)7
(8,11)(13

2
,25

2
)(7,14)(17

2
,27

2
)(19

2
,25

2
)(29

3
,12)(28

3
,11)
37

6
4

3
+5

2
2+3

2
10
563(2,12)5
(4,11)(0,11)(-2

3
,35

3
)(0,13)(2,13)
20

3
6+8

3
2+2

3
5
569(-4,12)5
(-5,12)(-5,14)(-4,14)(-3

2
,23

2
)(-3,10)
31

4
3+62
571(-6,12)5
(-6,11)(-8,11)(-47

7
,104

7
)(-5,14)(-5,12)
55

7
4+2+6

7
5+9

7
10
577(-12,12)5
(-13,12)(-13,10)(-23

2
,21

2
)(-41

4
,47

4
)(-11,14)
51

8
2+13

4
2+5

4
10
587(-12,2)4
(-13,2

3
)(-13,4)(-11,10

3
)(-11,0)
20

3
20

3
+4

3
10
593(-12,-4)5
(-25

2
,-5

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

4
,-25

4
)(-57

4
,-23

4
)(-53

4
,-11

4
)
17

2
32+5

2
10
599(-12,-10)6
(-13,-10)(-13,-8)(-23

2
,-17

2
)(-11,-9)(-11,-11)(-12,-11)
19

4
5+3

2
2+1

2
10
601(-12,-12)7
(-13,-12)(-13,-14)(-11,-14)(-10,-13)(-21

2
,-23

2
)(-11,-11)(-12,-11)
29

4
5+5

2
2+1

2
10
607(-6,-12)6
(-6,-13)(-15

2
,-23

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

2
,-23

2
)(-5,-13)
29

4
1+7

2
2+3

2
10
613(0,-12)8
(1,-13)(-2,-13)(-8

3
,-35

3
)(-2,-11)(1,-11)(3

2
,-23

2
)(5

3
,-12)(3

2
,-25

2
)
15

2
6+5

3
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