Prime p₀= 3091466380408238471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 16 2 130 2 40 2 58 2 208 2 (?)
a_n: 0 2 18 20 36 38 168 170 210 212 270 272 480 482
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: 482
Found by: L@MiR
db: batch=83, k=14, 16 16 130 40 58 208

SPT(16)	3091464572029624943	0 14 74 104 126 146 158 168 236 246 258 278 300 330 390 404	-1808378613528
SPT(16)	3091464619893981869	0 18 38 68 80 104 108 228 230 350 354 378 390 420 440 458	-1760514256602
STPT(10)	3091465146503760371	0 2 36 38 78 80 120 122 156 158	-1233904478100
SPT(16)	3091465328803901729	0 12 78 120 138 140 162 194 318 350 372 374 392 434 500 512	-1051604336742
SPT(16)	3091465577886583309	0 12 24 54 58 118 124 130 222 228 234 294 298 328 340 352	-802521655162
STPT(10)	3091465836847458659	0 2 78 80 120 122 162 164 240 242	-543560779812
SPT(16)	3091466568862962109	0 4 54 88 108 124 144 190 312 358 378 394 414 448 498 502	188454723638
SPT(16)	3091467052672370833	0 4 6 16 48 54 66 90 94 118 130 136 168 178 180 184	672264132362
SPT(16)	3091467176298922081	0 16 48 58 78 82 160 166 192 198 276 280 300 310 342 358	795890683610
STPT(10)	3091467329144141219	0 2 18 20 30 32 42 44 60 62	948735902748
SPT(16)	3091467740674489279	0 52 94 102 112 148 174 178 204 208 234 270 280 288 330 382	1360266250808