Prime p₀= 3034569003903979427 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 34 2 82 2 34 2 10 2 16 2 (?)
a_n: 0 2 54 56 90 92 174 176 210 212 222 224 240 242
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: [SG]ATA-Rolf
db: batch=82, k=14, 52 34 82 34 10 16

SPT(16)	3034568540344609897	0 16 24 52 54 84 154 172 234 252 322 352 354 382 390 406	-463559369530
STPT(10)	3034568577913432529	0 2 12 14 30 32 48 50 60 62	-425990546898
SPT(16)	3034568632353742837	0 22 70 82 90 94 160 166 360 366 432 436 444 456 504 526	-371550236590
SPT(16)	3034568675027813639	0 24 30 48 132 144 158 162 170 174 188 200 284 302 308 332	-328876165788
SPT(16)	3034568785076298521	0 32 50 62 86 150 162 198 260 296 308 372 396 408 426 458	-218827680906
TPT(14)	3034568936419539479	0 2 102 104 162 164 210 212 240 242 252 254 342 344	-67484439948
SPT(16)	3034569025723318819	0 10 24 28 84 102 112 142 150 180 190 208 264 268 282 292	21819339392
STPT(10)	3034569186668104661	0 2 36 38 78 80 120 122 156 158	182764125234
SPT(16)	3034569420371119349	0 14 24 80 120 140 182 192 242 252 294 314 354 410 420 434	416467139922
SPT(16)	3034570221813585853	0 30 54 88 136 198 264 286 318 340 406 468 516 550 574 604	1217909606426
STPT(10)	3034570646375881901	0 2 36 38 78 80 120 122 156 158	1642471902474