Prime p₀= 2420295244382921429 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 34 2 28 2 82 2 178 2 (?)
a_n: 0 2 42 44 102 104 138 140 168 170 252 254 432 434
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: 434
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 40 58 34 28 82 178

SPT(16)	2420292684288195799	0 34 42 70 118 174 208 264 328 384 418 474 522 550 558 592	-2560094725630
STPT(10)	2420293113788529137	0 2 42 44 132 134 222 224 264 266	-2130594392292
SPT(16)	2420293713622303643	0 18 24 90 150 168 180 200 258 278 290 308 368 434 440 458	-1530760617786
SPT(16)	2420293847131474367	0 30 120 170 182 230 270 282 284 296 336 384 396 446 536 566	-1397251447062
TPT(14)	2420294553631140839	0 2 48 50 72 74 78 80 210 212 312 314 342 344	-690751780590
SPT(16)	2420294701569856873	0 34 40 54 94 160 198 208 210 220 258 324 364 378 384 418	-542813064556
SPT(16)	2420295620867138621	0 6 48 50 90 96 126 150 176 200 230 236 276 278 320 326	376484217192
TPT(14)	2420295627957112649	0 2 18 20 30 32 72 74 78 80 132 134 162 164	383574191220
STPT(10)	2420296312938171719	0 2 18 20 30 32 42 44 60 62	1068555250290
SPT(16)	2420296499622103699	0 24 48 90 108 130 150 160 168 178 198 220 238 280 304 328	1255239182270
SPT(16)	2420296742432787677	0 26 32 60 90 96 162 180 182 200 266 272 302 330 336 362	1498049866248