Prime p₀= 2377449088966984631 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 94 2 88 2 88 2 88 2 10 2 (?)
a_n: 0 2 30 32 126 128 216 218 306 308 396 398 408 410
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: 410
Found by: Landjunge
db: batch=81, k=14, 28 94 88 88 88 10

SPT(16)	2377446575790424211	0 20 182 188 236 266 272 276 332 336 342 372 420 426 588 608	-2513176560420
TPT(14)	2377447868903775119	0 2 60 62 72 74 90 92 132 134 138 140 168 170	-1220063209512
SPT(16)	2377447986138949487	0 24 36 56 60 114 144 150 170 176 206 260 264 284 296 320	-1102828035144
STPT(10)	2377448124689881091	0 2 30 32 60 62 90 92 120 122	-964277103540
SPT(18)	2377448782316762351	0 32 72 98 150 170 176 186 240 248 302 312 318 338 390 416 456 488	-306650222280
SPT(16)	2377449009625404523	0 4 28 34 78 124 138 144 190 196 210 256 300 306 330 334	-79341580108
STPT(10)	2377449318413265527	0 2 30 32 72 74 114 116 144 146	229446280896
STPT(10)	2377449760609942157	0 2 60 62 72 74 84 86 144 146	671642957526
SPT(16)	2377450172096692411	0 12 28 66 78 102 112 118 180 186 196 220 232 270 286 298	1083129707780
SPT(16)	2377450285780300517	0 12 24 36 50 66 80 164 252 336 350 366 380 392 404 416	1196813315886
STPT(10)	2377450340955242381	0 2 6 8 48 50 90 92 96 98	1251988257750