Prime p₀= 2310503991036590537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 130 2 64 2 22 2 34 2 10 2 (?)
a_n: 0 2 12 14 144 146 210 212 234 236 270 272 282 284
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: 284
Found by: FritzB
db: batch=81, k=14, 10 130 64 22 34 10

SPT(16)	2310503013959620919	0 14 20 24 200 218 230 248 330 348 360 378 554 558 564 578	-977076969618
STPT(10)	2310503273208139349	0 2 18 20 30 32 42 44 60 62	-717828451188
STPT(10)	2310503286098523947	0 2 54 56 72 74 90 92 144 146	-704938066590
SPT(16)	2310503580145335637	0 52 66 76 90 126 130 154 192 216 220 256 270 280 294 346	-410891254900
SPT(16)	2310503691348116129	0 48 50 68 78 92 120 132 140 152 180 194 204 222 224 272	-299688474408
SPT(16)	2310503808687465557	0 12 60 80 102 110 122 134 210 222 234 242 264 284 332 344	-182349124980
SPT(16)	2310504203934876857	0 20 110 116 140 150 164 200 336 372 386 396 420 426 516 536	212898286320
STPT(10)	2310504279654312281	0 2 78 80 138 140 198 200 276 278	288617721744
SPT(16)	2310504426179391509	0 44 78 114 140 152 182 188 294 300 330 342 368 404 438 482	435142800972
TPT(14)	2310504430103111717	0 2 234 236 294 296 312 314 324 326 390 392 402 404	439066521180
SPT(16)	2310504533616452269	0 4 18 22 54 130 144 150 232 238 252 328 360 364 378 382	542579861732