Prime p₀= 3091245391301770607 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 22 2 16 2 76 2 130 2 (?)
a_n: 0 2 84 86 90 92 114 116 132 134 210 212 342 344
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: 344
Found by: TheKillerChicken
db: batch=83, k=14, 82 4 22 16 76 130

SPT(16)	3091243609601863943	0 24 68 78 80 110 168 188 210 230 288 318 320 330 374 398	-1781699906664
STPT(10)	3091244057070115151	0 2 6 8 18 20 30 32 36 38	-1334231655456
STPT(12)	3091244579759990987	0 2 12 14 90 92 132 134 210 212 222 224	-811541779620
STPT(10)	3091244717112556967	0 2 30 32 42 44 54 56 84 86	-674189213640
SPT(16)	3091244855880567853	0 36 84 120 124 190 238 294 340 396 444 510 514 550 598 634	-535421202754
STPT(10)	3091244927150002121	0 2 36 38 78 80 120 122 156 158	-464151768486
SPT(16)	3091245534461841437	0 24 30 36 72 90 92 102 104 114 116 134 170 176 182 206	143160070830
SPT(16)	3091246184800682977	0 70 82 90 120 132 190 204 220 234 292 304 334 342 354 424	793498912370
SPT(16)	3091246257904904849	0 14 78 98 120 138 140 278 294 432 434 452 474 494 558 572	866603134242
SPT(16)	3091247158643061637	0 22 42 46 112 114 142 156 160 174 202 204 270 274 294 316	1767341291030
SPT(16)	3091247244536282929	0 30 52 60 82 132 144 154 198 208 220 270 292 300 322 352	1853234512322