Prime p₀= 950540812627589627 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 172 2 76 2 10 2 46 2 70 2 (?)
a_n: 0 2 120 122 294 296 372 374 384 386 432 434 504 506
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: 506
Found by: Theadalus
db: batch=76, k=14, 118 172 76 10 46 70

SPT(16)	950539973091625459	0 22 28 48 78 90 130 132 160 162 202 214 244 264 270 292	-839535964168
SPT(16)	950540267993300191	0 28 30 42 48 120 132 138 142 148 160 232 238 250 252 280	-544634289436
STPT(10)	950540294709008369	0 2 42 44 60 62 78 80 120 122	-517918581258
SPT(16)	950540573905494961	0 6 58 88 96 148 160 162 166 168 180 232 240 270 322 328	-238722094666
SPT(16)	950540616851737871	0 102 116 122 150 156 198 212 306 320 362 368 396 402 416 518	-195775851756
SPT(16)	950540773654365479	0 14 18 32 62 80 132 144 188 200 252 270 300 314 318 332	-38973224148
SPT(16)	950540975821349219	0 30 48 54 80 84 98 102 110 114 128 132 158 164 182 212	163193759592
STPT(10)	950541865024859201	0 2 6 8 48 50 90 92 96 98	1052397269574
TPT(14)	950541914947452431	0 2 6 8 30 32 246 248 258 260 288 290 378 380	1102319862804
STPT(10)	950541990528190691	0 2 36 38 78 80 120 122 156 158	1177900601064
SPT(16)	950542016634387137	0 20 24 32 60 90 134 174 200 240 284 314 342 350 354 374	1204006797510