Voronoi Diagrams of the Ulam Prime Spiral


The table below shows the primes that have 'less round' Voronoi cells than any smaller prime. I conjecture that this sequence is an infinite sequence - that is, there's no 'least round' 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(P/2)2/A
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
4.132018689726583
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
4.237705522975003
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
4.821635921280641
31(3,3)4
(2,3)(3,2)(4,2)(4,5)
7

2
4+32
4.852937535496735
47(1,-3)4
(-1,-4)(3

2
,-3

2
)(3,-2)(1

2
,-9

2
)
5
52+10
5.236067977499791
181(7,5)4
(7,4)(14

3
,19

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

3
2+16

3
2+2

3
5
5.706147946283363
229(8,-4)4
(6,-5)(9,-2)(9,-4)(8,-5)
4
4+42
5.82842712474619
1669(8,-20)3
(7,-21)(7,-18)(10,-21)
9

2
6+32
5.828427124746191
2153(-23,-13)5
(-24,-13)(-24,-15)(-62

3
,-35

3
)(-167

8
,-85

8
)(-22,-11)
143

24
2+16

3
2+3

8
10+5

24
26
5.832955450142133
4603(-12,34)6
(-14,35)(-11,32)(-10,33)(-14,37)(-43

3
,37)(-29

2
,73

2
)
91

12
1

3
+82+2

3
10
6.2375692795404465
5861(-30,-38)4
(-32,-39)(-28,-35)(-83

3
,-110

3
)(-30,-39)
19

3
2+19

3
2+1

3
26
6.32302992683966