Prime p₀= 2591867556168223439 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 148 2 4 2 10 2 118 2 58 2 (?)
a_n: 0 2 42 44 192 194 198 200 210 212 330 332 390 392
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: 392
Found by: JayPi
db: batch=82, k=14, 40 148 4 10 118 58

SPT(16)	2591866625792187529	0 42 60 88 130 142 162 168 214 220 240 252 294 322 340 382	-930376035910
SPT(16)	2591866667013639997	0 46 64 102 112 120 156 172 174 190 226 234 244 282 300 346	-889154583442
STPT(10)	2591866838391166619	0 2 48 50 90 92 132 134 180 182	-717777056820
SPT(16)	2591866844386334833	0 24 48 54 120 156 180 198 216 234 258 294 360 366 390 414	-711781888606
STPT(10)	2591866972753529291	0 2 168 170 198 200 228 230 396 398	-583414694148
SPT(16)	2591867481102276791	0 68 78 96 110 120 140 152 186 198 218 228 242 260 270 338	-75065946648
SPT(16)	2591867564456403943	0 34 40 58 124 138 156 166 168 178 196 210 276 294 300 334	8288180504
SPT(16)	2591867695100066309	0 50 62 78 90 128 132 134 168 170 174 212 224 240 252 302	138931842870
STPT(10)	2591867726408997677	0 2 84 86 132 134 180 182 264 266	170240774238
SPT(16)	2591868953764897561	0 16 66 82 156 166 208 222 226 240 282 292 366 382 432 448	1397596674122
SPT(16)	2591868968543833351	0 28 42 52 58 118 172 192 196 216 270 330 336 346 360 388	1412375609912