Possible Prime Constellation Patterns

From Riecoin

Here is a list of all the possible prime constellation patterns, up to 24-tuples[1].

Note that no constellation of length 24 is known, and the unique ones known for 22 and 23 are trivial.

Riecoin uses 7-tuples starting from the second fork (formerly 6-tuples) for Mainnet and 5-tuples (formerly 4-tuples) for Testnet.

Tables as a text file.

Length Offset from start
1 0
2 0, 2
3 0, 2, 6
3 0, 4, 6
4 0, 2, 6, 8
5 0, 2, 6, 8, 12
5 0, 4, 6, 10, 12
6 0, 4, 6, 10, 12, 16
7 0, 2, 6, 8, 12, 18, 20
7 0, 2, 8, 12, 14, 18, 20
8 0, 2, 6, 8, 12, 18, 20, 26
8 0, 2, 6, 12, 14, 20, 24, 26
8 0, 6, 8, 14, 18, 20, 24, 26
9 0, 2, 6, 8, 12, 18, 20, 26, 30
9 0, 2, 6, 12, 14, 20, 24, 26, 30
9 0, 4, 6, 10, 16, 18, 24, 28, 30
9 0, 4, 10, 12, 18, 22, 24, 28, 30
10 0, 2, 6, 8, 12, 18, 20, 26, 30, 32
10 0, 2, 6, 12, 14, 20, 24, 26, 30, 32
11 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36
11 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36
12 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42
12 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42
13 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48
13 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48
13 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48
13 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48
13 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48
13 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48
14 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50
14 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50
15 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56
15 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56
15 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56
15 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56
16 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60
16 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60
17 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66
17 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66
17 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66
17 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66
18 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
18 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
19 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76
19 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76
19 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76
19 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
20 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80
20 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80
21 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84
21 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84
22 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80, 86, 90
22 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 90
22 0, 4, 10, 12, 18, 22, 24, 28, 34, 40, 42, 48, 52, 54, 60, 64, 70, 78, 82, 84, 88, 90
22 0, 6, 8, 14, 18, 20, 24, 30, 36, 38, 44, 48, 50, 56, 60, 66, 74, 78, 80, 84, 86, 90
23 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 90, 94
23 0, 4, 10, 12, 18, 22, 24, 28, 34, 40, 42, 48, 52, 54, 60, 64, 70, 78, 82, 84, 88, 90, 94
24 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 60, 66, 70, 72, 76, 82, 84, 90, 94, 96, 100
24 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76, 84, 88, 94, 96, 100
24 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 48, 54, 58, 60, 66, 70, 76, 84, 88, 90, 94, 96, 100
24 0, 4, 6, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 90, 94, 96, 100

Here are the same constellations, but with non cumulative offsets (useful in some configuration files and implementations).

Length Offset differences
1 0
2 0, 2
3 0, 2, 4
3 0, 4, 2
4 0, 2, 4, 2
5 0, 2, 4, 2, 4
5 0, 4, 2, 4, 2
6 0, 4, 2, 4, 2, 4
7 0, 2, 4, 2, 4, 6, 2
7 0, 2, 6, 4, 2, 4, 2
8 0, 2, 4, 2, 4, 6, 2, 6
8 0, 2, 4, 6, 2, 6, 4, 2
8 0, 6, 2, 6, 4, 2, 4, 2
9 0, 2, 4, 2, 4, 6, 2, 6, 4
9 0, 2, 4, 6, 2, 6, 4, 2, 4
9 0, 4, 2, 4, 6, 2, 6, 4, 2
9 0, 4, 6, 2, 6, 4, 2, 4, 2
10 0, 2, 4, 2, 4, 6, 2, 6, 4, 2
10 0, 2, 4, 6, 2, 6, 4, 2, 4, 2
11 0, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4
11 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2
12 0, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6
12 0, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2
13 0, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6
13 0, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4
13 0, 2, 10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4
13 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2
13 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2
13 0, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2
14 0, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2
14 0, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2
15 0, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6
15 0, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2
15 0, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2
15 0, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2
16 0, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4
16 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2
17 0, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4
17 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6
17 0, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2
17 0, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4
18 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4
18 0, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4
19 0, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4
19 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6
19 0, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4
19 0, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4
20 0, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2
20 0, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2
21 0, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4
21 0, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2
22 0, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4
22 0, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6
22 0, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2
22 0, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4
23 0, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4
23 0, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4
24 0, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 8, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4
24 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 6, 2, 4
24 0, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 8, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4
24 0, 4, 2, 6, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4

References