Prime p₀= 4327911187118258021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 40 2 46 2 70 2 40 2 (?)
a_n: 0 2 6 8 36 38 78 80 126 128 198 200 240 242
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: 242
Found by: Agostino
db: batch=85, k=14, 4 28 40 46 70 40

SPT(16)	4327909430568935737	0 4 10 40 60 82 84 130 276 322 324 346 366 396 402 406	-1756549322284
SPT(16)	4327909448504401043	0 30 48 86 114 186 224 254 270 300 338 410 438 476 494 524	-1738613856978
SPT(16)	4327909598172009197	0 32 74 90 110 144 150 162 164 176 182 216 236 252 294 326	-1588946248824
TPT(16)	4327909960507282139	0 2 42 44 48 50 102 104 132 134 342 344 378 380 390 392	-1226610975882
SPT(16)	4327910065143252989	0 8 14 20 32 90 140 144 188 192 242 300 312 318 324 332	-1121975005032
SPT(16)	4327910681251937383	0 18 64 66 70 88 114 148 156 190 216 234 238 240 286 304	-505866320638
SPT(16)	4327911772055950567	0 30 54 126 130 142 150 186 220 256 264 276 280 352 376 406	584937692546
SPT(16)	4327912142804680103	0 98 116 126 186 198 204 224 330 350 356 368 428 438 456 554	955686422082
STPT(10)	4327912217139377549	0 2 12 14 90 92 168 170 180 182	1030021119528
SPT(16)	4327912859769858607	0 66 94 120 132 136 150 156 160 166 180 184 196 222 250 316	1672651600586
SPT(16)	4327912899473858119	0 12 90 102 112 130 138 174 208 244 252 270 280 292 370 382	1712355600098