Prime p₀= 2341127913268628021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 40 2 100 2 94 2 208 2 10 2 (?)
a_n: 0 2 126 128 168 170 270 272 366 368 576 578 588 590
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: 590
Found by: Xenon
db: batch=81, k=14, 124 40 100 94 208 10

SPT(16)	2341126783105127887	0 42 64 70 106 114 154 156 190 192 232 240 276 282 304 346	-1130163500134
SPT(16)	2341126856346137411	0 2 18 56 68 102 146 156 182 192 236 270 282 320 336 338	-1056922490610
SPT(16)	2341127027885394389	0 2 68 90 102 104 132 174 278 320 348 350 362 384 450 452	-885383233632
SPT(16)	2341127114847229699	0 72 82 118 124 174 180 222 370 412 418 468 474 510 520 592	-798421398322
STPT(10)	2341127224558346051	0 2 36 38 78 80 120 122 156 158	-688710281970
STPT(10)	2341127387465367197	0 2 12 14 72 74 132 134 144 146	-525803260824
SPT(16)	2341127941447145339	0 14 32 90 140 158 194 212 240 258 294 312 362 420 438 452	28178517318
SPT(16)	2341127998490870219	0 8 38 60 92 134 138 152 210 224 228 270 302 324 354 362	85222242198
STPT(10)	2341128066399557129	0 2 30 32 60 62 90 92 120 122	153130929108
SPT(16)	2341128206791507747	0 22 120 126 136 150 172 196 336 360 382 396 406 412 510 532	293522879726
STPT(10)	2341128418868536049	0 2 18 20 30 32 42 44 60 62	505599908028