Prime p₀= 1176021842189014319 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 4 2 40 2 136 2 82 2 28 2 (?)
a_n: 0 2 42 44 48 50 90 92 228 230 312 314 342 344
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: 344
Found by: Theadalus
db: batch=77, k=14, 40 4 40 136 82 28

SPT(16)	1176021480721653823	0 24 46 64 66 138 178 204 220 246 286 358 360 378 400 424	-361467360496
SPT(16)	1176021556642091683	0 6 10 28 88 118 160 210 226 276 318 348 408 426 430 436	-285546922636
SPT(16)	1176021710837774993	0 36 38 56 96 126 168 176 210 218 260 290 330 348 350 386	-131351239326
SPT(16)	1176021717595565051	0 2 12 50 68 80 102 122 156 176 198 210 228 266 276 278	-124593449268
SPT(16)	1176021795699962609	0 24 48 54 62 68 72 114 248 290 294 300 308 314 338 362	-46489051710
SPT(16)	1176021812020426429	0 4 28 42 58 90 102 120 142 160 172 204 220 234 258 262	-30168587890
TPT(14)	1176021958984794599	0 2 12 14 18 20 42 44 138 140 240 242 402 404	116795780280
STPT(10)	1176022143557347781	0 2 30 32 60 62 90 92 120 122	301368333462
SPT(16)	1176022333750893593	0 26 48 66 86 96 138 156 308 326 368 378 398 416 438 464	491561879274
STPT(10)	1176022491517363541	0 2 6 8 18 20 30 32 36 38	649328349222
SPT(16)	1176022571813407393	0 34 48 54 76 130 138 154 180 196 204 258 280 286 300 334	729624393074