Initial members of "L - consecutive prime k-tuplets with the smallest possible and constant gap (D)"
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last updated: 26 Jan 2022
Consecutive Prime Twins | ||
L | D | First initial members |
2 | 6 | [ 5 + d , d = 0, 2 ] + 6•n , n = 0 .. 1 |
3 | 12 | [ 5 + d , d = 0, 2 ] + 12•n , n = 0 .. 2 |
4 | 30 | [ 11 + d , d = 0, 2 ] + 30•n , n = 0 .. 3 |
5 | 30 | [ 1702218611 + d , d = 0, 2 ] + 30•n ; n = 0 .. 4 |
6 | 210 | [ 3057117407 + d , d = 0, 2 ] + 210•n ; n = 0 .. 5 |
7 | 210 | [ 66583737656789 + d , d = 0, 2 ] + 210•n ; n = 0 .. 6 |
Consecutive Prime Triplets | ||
L | D | First initial members |
2 | 6 6 |
[ 5 + d , d = 0, 2, 6 ] + 6•n , n = 0 .. 1 [ 7 + d , d = 0, 4, 6 ] + 6•n , n = 0 .. 1 |
3 | 30 30 |
[ 97547 + d , d = 0, 2, 6 ] + 30•n ; n = 0 .. 2 [ 7 + d , d = 0, 4, 6 ] + 30•n , n = 0 .. 2 |
4 | 210 210 |
[ 38680961771 + d , d = 0, 2, 6 ] + 210•n ; n = 0 .. 3 [ 2783876437 + d , d = 0, 4, 6 ] + 210•n ; n = 0 .. 3 |
5 | 420 420 |
[ 1063383716622671 + d , d = 0, 2, 6 ] + 420•n ; n = 0 .. 4 [ 366943408969447 + d , d = 0, 4, 6 ] + 420•n ; n = 0 .. 4 |
Consecutive Prime Quadruplets | ||
L | D | First initial members |
2 | 30 | [ 1006301 + d , d = 0, 2, 6, 8 ] + 30•n , n = 0 .. 1 |
3 | 90 | [ 11 + d , d = 0, 2, 6, 8 ] + 90•n , n = 0 .. 2 |
4 | 420 | [ 6234140990672051 + d , d = 0, 2, 6, 8 ] + 420•n , n = 0 .. 3 |
Consecutive Prime Quintuplets | ||
L | D | First initial members |
2 | 90 90 |
[ 11 + d , d = 0, 2, 6, 8, 12 ] + 90•n , n = 0 .. 1 [ 7 + d , d = 0, 4, 6, 10, 12 ] + 90•n , n = 0 .. 1 |
3 | 210 210 |
[ 24097678829994941 + d , d = 0, 2, 6, 8, 12 ] + 210•n , n = 0 .. 2 [ 74426354260647787 + d , d = 0, 4, 6, 10, 12 ] + 210•n , n = 0 .. 2 |
Consecutive Prime Sextuplets | ||
L | D | First initial members |
2 | 210 | [ 5835906544537 + d , d = 0, 4, 6, 10, 12, 16 ] + 210•n , n = 0 .. 1 |
3 | 210 | [ 50038627250687303646277 + d , d = 0, 4, 6, 10, 12, 16 ] + 210•n , n = 0 .. 2 ( found by Jörg Waldvogel & Peter Leikauf ) |
Consecutive Prime Septuplets | ||
L | D | First initial members |
2 | 210 210 |
[ 1683059174212301 + d , d = 0, 2, 6, 8, 12, 18, 20 ] + 210•n , n = 0 .. 1 [ 482046424357019 + d , d = 0, 2, 8, 12, 14, 18, 20 ] + 210•n , n = 0 .. 1 |
Consecutive Prime Octuplets | ||
L | D | First initial members |
2 | 60 420 420 |
[ 10458834002271815117 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 ] + 60•n , n = 0 .. 1 [ 7387829334225124901 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 ] + 420•n , n = 0 .. 1 [ 1365135293377079663 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 ] + 420•n , n = 0 .. 1 |
Consecutive Prime Nonuplets | ||
L | D | First initial members |
2 | 60 | [ 54014646858393564373 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 ] + 60•n , n = 0 .. 1 ( found by Jörg Waldvogel & Peter Leikauf ) |