Prime p₀= 3091514537501670431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 22 2 94 2 10 2 16 2 58 2 (?)
a_n: 0 2 6 8 30 32 126 128 138 140 156 158 216 218
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 218
Found by: L@MiR
db: batch=83, k=14, 4 22 94 10 16 58

TPT(14)	3091512351331188599	0 2 12 14 48 50 90 92 150 152 168 170 222 224	-2186170481832
STPT(10)	3091512666069816617	0 2 30 32 72 74 114 116 144 146	-1871431853814
SPT(16)	3091512666703508423	0 6 24 48 78 80 90 134 180 224 234 236 266 290 308 314	-1870798162008
STPT(10)	3091512667174811681	0 2 6 8 48 50 90 92 96 98	-1870326858750
SPT(16)	3091513509104258869	0 22 24 72 88 114 154 190 192 228 268 294 310 358 360 382	-1028397411562
STPT(10)	3091514349011247947	0 2 60 62 72 74 84 86 144 146	-188490422484
STPT(12)	3091514547832823219	0 2 30 32 48 50 72 74 90 92 120 122	10331152788
SPT(16)	3091514645063948429	0 14 18 60 98 128 138 170 228 260 270 300 338 380 384 398	107562277998
SPT(16)	3091514785008382501	0 46 58 66 88 136 168 222 226 280 312 360 382 390 402 448	247506712070
STPT(10)	3091514925860172347	0 2 30 32 42 44 54 56 84 86	388358501916
SPT(16)	3091515277097623819	0 18 48 58 60 78 108 154 234 280 310 328 330 340 370 388	739595953388