Prime p₀= 944376175678012841 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 70 2 178 2 16 2 40 2 58 2 (?)
a_n: 0 2 36 38 108 110 288 290 306 308 348 350 408 410
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: 410
Found by: HenkM
db: batch=76, k=14, 34 70 178 16 40 58

SPT(16)	944374582423982123	0 8 18 24 66 108 116 140 144 168 176 218 260 266 276 284	-1593254030718
SPT(16)	944374879674875249	0 2 14 24 30 80 200 212 480 492 612 662 668 678 690 692	-1296003137592
SPT(16)	944374894805102027	0 12 14 42 60 72 80 114 122 156 164 176 194 222 224 236	-1280872910814
SPT(16)	944375778415626097	0 16 46 66 84 94 154 156 184 186 246 256 274 294 324 340	-397262386744
TPT(14)	944375809099678979	0 2 18 20 48 50 132 134 240 242 270 272 282 284	-366578333862
SPT(16)	944375870932307453	0 56 128 156 198 246 258 288 356 386 398 446 488 516 588 644	-304745705388
TPT(14)	944376547301382539	0 2 12 14 120 122 168 170 180 182 210 212 282 284	371623369698
SPT(16)	944376767346898261	0 10 36 90 138 150 180 246 292 358 388 400 448 502 528 538	591668885420
SPT(16)	944376889222554883	0 124 130 174 184 186 270 286 294 310 394 396 406 450 456 580	713544542042
SPT(16)	944377098294460433	0 14 26 30 38 54 74 80 144 150 170 186 194 198 210 224	922616447592
SPT(16)	944377199023118141	0 8 56 66 150 218 228 260 276 308 318 386 470 480 528 536	1023345105300