Prime p₀= 2727859020437584001 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 76 2 10 2 10 2 16 2 (?)
a_n: 0 2 36 38 48 50 126 128 138 140 150 152 168 170
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: 170
Found by: JayPi
db: batch=82, k=14, 34 10 76 10 10 16

SPT(16)	2727857899390379257	0 22 42 60 84 126 132 144 262 274 280 322 346 364 384 406	-1121047204744
SPT(16)	2727857904059527669	0 22 42 48 58 132 138 162 238 262 268 342 352 358 378 400	-1116378056332
SPT(16)	2727858152835410501	0 48 86 90 96 140 158 180 188 210 228 272 278 282 320 368	-867602173500
SPT(16)	2727858442248432439	0 4 94 118 144 190 228 238 360 370 408 454 480 504 594 598	-578189151562
STPT(10)	2727858743549447537	0 2 12 14 42 44 72 74 84 86	-276888136464
SPT(16)	2727858794030191361	0 8 36 42 56 86 128 138 140 150 192 222 236 242 270 278	-226407392640
SPT(16)	2727859611727509659	0 24 38 92 140 144 158 170 192 204 218 222 270 324 338 362	591289925658
STPT(10)	2727859672541143667	0 2 90 92 102 104 114 116 204 206	652103559666
SPT(16)	2727859674781638377	0 2 102 120 134 182 200 204 290 294 312 360 374 392 492 494	654344054376
SPT(16)	2727859728551375477	0 20 26 30 72 140 170 212 300 342 372 440 482 486 492 512	708113791476
STPT(10)	2727859873407608879	0 2 18 20 30 32 42 44 60 62	852970024878