Initial members of "L - consecutive prime k-tuplets with the smallest possible and constant gap (D)"

←
last updated: 26 Jan 2022

Consecutive Prime Twins
 L  D  First initial members
 2  6  [ 5 + d , d = 0, 2 ] + 6n , n = 0 .. 1
 3  12  [ 5 + d , d = 0, 2 ] + 12n , n = 0 .. 2
 4  30  [ 11 + d , d = 0, 2 ] + 30n , n = 0 .. 3
 5  30  [ 1702218611 + d , d = 0, 2 ] + 30n ; n = 0 .. 4
 6  210  [ 3057117407 + d , d = 0, 2 ] + 210n ; n = 0 .. 5
 7  210  [ 66583737656789 + d , d = 0, 2 ] + 210n ; n = 0 .. 6

Consecutive Prime Triplets
 L  D  First initial members
 2  6
 6		  [ 5 + d , d = 0, 2, 6 ] + 6n , n = 0 .. 1
 [ 7 + d , d = 0, 4, 6 ] + 6n , n = 0 .. 1
 3  30
 30		  [ 97547 + d , d = 0, 2, 6 ] + 30n ; n = 0 .. 2
 [ 7 + d , d = 0, 4, 6 ] + 30n , n = 0 .. 2
 4  210
 210		  [ 38680961771 + d , d = 0, 2, 6 ] + 210n ; n = 0 .. 3
 [ 2783876437 + d , d = 0, 4, 6 ] + 210n ; n = 0 .. 3
 5  420
 420		  [ 1063383716622671 + d , d = 0, 2, 6 ] + 420n ; n = 0 .. 4
 [ 366943408969447 + d , d = 0, 4, 6 ] + 420n ; n = 0 .. 4

Consecutive Prime Quadruplets
 L  D  First initial members
 2  30  [ 1006301 + d , d = 0, 2, 6, 8 ] + 30n , n = 0 .. 1
 3  90  [ 11 + d , d = 0, 2, 6, 8 ] + 90n , n = 0 .. 2
 4  420  [ 6234140990672051 + d , d = 0, 2, 6, 8 ] + 420n , n = 0 .. 3

Consecutive Prime Quintuplets
 L  D  First initial members
 2  90
 90		  [ 11 + d , d = 0, 2, 6, 8, 12 ] + 90n , n = 0 .. 1
 [ 7 + d , d = 0, 4, 6, 10, 12 ] + 90n , n = 0 .. 1
 3  210
 210		  [ 24097678829994941 + d , d = 0, 2, 6, 8, 12 ] + 210n , n = 0 .. 2
 [ 74426354260647787 + d , d = 0, 4, 6, 10, 12 ] + 210n , n = 0 .. 2

Consecutive Prime Sextuplets
 L  D  First initial members
 2  210  [ 5835906544537 + d , d = 0, 4, 6, 10, 12, 16 ] + 210n , n = 0 .. 1
 3  210  [ 50038627250687303646277 + d , d = 0, 4, 6, 10, 12, 16 ] + 210n , 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 ] + 210n , n = 0 .. 1
 [ 482046424357019 + d , d = 0, 2, 8, 12, 14, 18, 20 ] + 210n , 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 ] + 60n , n = 0 .. 1
 [ 7387829334225124901 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 ] + 420n , n = 0 .. 1
 [ 1365135293377079663 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 ] + 420n , 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 ] + 60n , n = 0 .. 1 ( found by Jörg Waldvogel & Peter Leikauf )