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

Consecutive Prime Twins
L D First initial members Pattern d Pattern  Z When Who
2 6  [ 5 + d ] +  Z d = 0, 2  Z = 0, 6
3 18  [ 11 + d ] +  Z
 [ 179 + d ] +  Z 		d = 0, 2  Z = 0, 6, 18
 Z = 0, 12, 18
4 30  [ 11 + d ] +  Z
 [ 626597 + d ] +  Z 		d = 0, 2  Z = 0, 6, 18, 30
 Z = 0, 12, 24, 30
5 36  [ 39713433671 + d ] +  Z d = 0, 2  Z = 0, 6, 18, 30, 36
6 48  [ 1256522812841 + d ] +  Z
 [ 45183473856329 + d ] +  Z 		d = 0, 2  Z = 0, 6, 18, 30, 36, 48
 Z = 0, 12, 18, 30, 42, 48
7 60  [ 1135141716537971 + d ] +  Z
 [ 9725353586573267 + d ] +  Z 		d = 0, 2  Z = 0, 6, 18, 30, 36, 48, 60
 Z = 0, 12, 24, 30, 42, 54, 60
8 84  [ 969971533709583960197 + d ] +  Z
 [ 865740639783851560847 + d ] +  Z 		d = 0, 2  Z = 0, 12, 24, 30, 42, 54, 60, 84
 Z = 0, 24, 30, 42, 54, 60, 72, 84
9 102  [ 35902987875008630158997 + d ] +  Z
 [ 670962238726376003928317 + d ] +  Z
 [ 1063660630652819772482009 + d ] +  Z
 [ 39582971901830749382519 + d ] +  Z 		d = 0, 2  Z = 0, 12, 30, 42, 54, 60, 84, 90, 102
 Z = 0, 12, 24, 30, 42, 54, 60, 84, 102
 Z = 0, 18, 42, 48, 60, 72, 78, 90, 102
 Z = 0, 12, 18, 42, 48, 60, 72, 90, 102 		2015 Jörg Waldvogel & Peter Leikauf

Consecutive Prime Triplets
L D First initial members Pattern d Pattern  Z When Who
2 6  [ 5 + d ] +  Z
 [ 7 + d ] +  Z 		d = 0, 2, 6
d = 0, 4, 6		  Z = 0, 6
 Z = 0, 6
3 30  [ 11 + d ] +  Z
 [ 1230343 + d ] +  Z 		d = 0, 2, 6
d = 0, 4, 6		  Z = 0, 6, 30
 Z = 0, 24, 30
4 60  [ 1367736257 + d ] +  Z
 [ 3676712951 + d ] +  Z
 [ 228847463227 + d ] +  Z
 [ 65455701733 + d ] +  Z 		d = 0, 2, 6
d = 0, 2, 6
d = 0, 4, 6
d = 0, 4, 6		  Z = 0, 24, 54, 60
 Z = 0, 30, 36, 60
 Z = 0, 6, 36, 60
 Z = 0, 24, 30, 60
5 84  [ 98538255329487707 + d ] +  Z
 [ 1515672991269843583 + d ] +  Z 		d = 0, 2, 6
d = 0, 4, 6		  Z = 0, 24, 54, 60, 84
 Z = 0, 24, 30, 60, 84

Consecutive Prime Quadruplets
L D First initial members Pattern d Pattern  Z When Who
2 30  [ 1006301 + d ] +  Z d = 0, 2, 6, 8  Z = 0, 30
3 120  [ 282005261771 + d ] +  Z
 [ 31007639083781 + d ] +  Z 		d = 0, 2, 6, 8  Z = 0, 30, 120
 Z = 0, 90, 120
4 210  [ 3051450534439926131 + d ] +  Z
 [ 300000224101777931 + d ] +  Z 		d = 0, 2, 6, 8  Z = 0, 30, 120, 210
 Z = 0, 90, 180, 210		 2015 Jörg Waldvogel & Peter Leikauf

Consecutive Prime Quintuplets
L D First initial members Pattern d Pattern  Z When Who
2 90  [ 11 + d ] +  Z
 [ 7 + d ] +  Z 		d = 0, 2, 6, 8, 12
d = 0, 4, 6, 10, 12		  Z = 0, 90
 Z = 0, 90
3 210  [ 2478508456517985161 + d ] +  Z
 [ 1830711463147481141 + d ] +  Z
 [ 1044428370657137017 + d ] +  Z
 [ 89997702037281547 + d ] +  Z 		d = 0, 2, 6, 8, 12
d = 0, 2, 6, 8, 12
d = 0, 4, 6, 10, 12
d = 0, 4, 6, 10, 12		  Z = 0, 90, 210
 Z = 0, 120, 210
 Z = 0, 90, 210
 Z = 0, 120, 210