Prime p₀= 2378170095046801667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 118 2 10 2 34 2 172 2 28 2 (?)
a_n: 0 2 42 44 162 164 174 176 210 212 384 386 414 416
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: 416
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 40 118 10 34 172 28

STPT(10)	2378168988892206467	0 2 60 62 72 74 84 86 144 146	-1106154595200
TPT(14)	2378168991439918139	0 2 138 140 210 212 288 290 372 374 390 392 402 404	-1103606883528
SPT(16)	2378169095936563651	0 36 88 198 252 270 276 306 322 352 358 376 430 540 592 628	-999110238016
STPT(10)	2378169268018454921	0 2 6 8 48 50 90 92 96 98	-827028346746
SPT(16)	2378169551151717751	0 18 22 28 30 36 52 88 120 156 172 178 180 186 190 208	-543895083916
SPT(16)	2378169948171670007	0 6 66 90 174 182 194 216 350 372 384 392 476 500 560 566	-146875131660
SPT(16)	2378170191544757143	0 10 18 48 94 100 114 160 354 400 414 420 466 496 504 514	96497955476
SPT(16)	2378170214746548283	0 6 36 118 120 154 166 208 246 288 300 334 336 418 448 454	119699746616
TPT(14)	2378170244118866081	0 2 150 152 276 278 390 392 528 530 588 590 630 632	149072064414
SPT(16)	2378170506170778461	0 2 6 62 158 176 200 212 216 228 252 270 366 422 426 428	411123976794
SPT(16)	2378170547388058853	0 20 26 44 80 86 104 126 134 156 174 180 216 234 240 260	452341257186