Prime p₀= 2336126491028012141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 4 2 58 2 28 2 28 2 (?)
a_n: 0 2 30 32 90 92 96 98 156 158 186 188 216 218
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: 218
Found by: Landjunge
db: batch=81, k=14, 28 58 4 58 28 28

SPT(16)	2336124999923258977	0 24 34 52 76 96 112 142 234 264 280 300 324 342 352 376	-1491104753164
SPT(18)	2336125003272259663	0 10 24 28 36 60 88 90 136 168 214 216 244 268 276 280 294 304	-1487755752478
STPT(10)	2336125419540202889	0 2 18 20 30 32 42 44 60 62	-1071487809252
SPT(16)	2336125563176795561	0 2 8 26 36 62 78 152 156 230 246 272 282 300 306 308	-927851216580
SPT(16)	2336125827400428179	0 12 32 50 72 90 98 110 120 132 140 158 180 198 218 230	-663627583962
SPT(16)	2336126286890014243	0 4 30 66 100 120 144 184 330 370 394 414 448 484 510 514	-204137997898
STPT(12)	2336126491028012141	0 2 30 32 90 92 96 98 156 158 186 188	0
SPT(16)	2336126494517713277	0 32 56 84 92 102 116 122 144 150 164 174 182 210 234 266	3489701136
SPT(13)	2336126714407597747	0 12 42 60 72 102 126 150 180 192 210 240 252	223379585606
SPT(16)	2336127141671247649	0 30 40 60 70 82 102 114 130 142 162 174 184 204 214 244	650643235508
STPT(10)	2336127517950190631	0 2 6 8 18 20 30 32 36 38	1026922178490