Prime p₀= 2324031820400233301 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 16 2 16 2 52 2 76 2 88 2 (?)
a_n: 0 2 120 122 138 140 156 158 210 212 288 290 378 380
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: 380
Found by: Landjunge
db: batch=81, k=14, 118 16 16 52 76 88

SPT(16)	2324030086699431763	0 24 66 168 186 210 228 276 298 346 364 388 406 508 550 574	-1733700801538
STPT(10)	2324030331244867541	0 2 6 8 18 20 30 32 36 38	-1489155365760
SPT(16)	2324031079114334963	0 14 24 36 44 84 126 128 156 158 200 240 248 260 270 284	-741285898338
STPT(10)	2324031598650437189	0 2 48 50 90 92 132 134 180 182	-221749796112
SPT(16)	2324031599697257459	0 78 120 140 158 170 188 228 242 282 300 312 330 350 392 470	-220702975842
SPT(16)	2324031802910368129	0 18 82 108 178 192 208 210 262 264 280 294 364 390 454 472	-17489865172
STPT(10)	2324031931236906731	0 2 36 38 78 80 120 122 156 158	110836673430
SPT(16)	2324032263336498703	0 16 36 88 118 130 196 234 280 318 384 396 426 478 498 514	442936265402
SPT(16)	2324032458969697951	0 52 66 70 88 90 96 118 150 172 178 180 198 202 216 268	638569464650
SPT(16)	2324032546107520693	0 40 46 76 186 198 210 240 256 286 298 310 420 450 456 496	725707287392
TPT(14)	2324032582714242689	0 2 18 20 240 242 252 254 330 332 378 380 408 410	762314009388