Prime p₀= 2234265458796178667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 166 2 40 2 4 2 40 2 (?)
a_n: 0 2 30 32 54 56 222 224 264 266 270 272 312 314
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: 314
Found by: Landjunge
db: batch=81, k=14, 28 22 166 40 4 40

SPT(16)	2234263880389503497	0 12 36 72 110 126 150 176 210 236 260 276 314 350 374 386	-1578406675170
SPT(16)	2234264035617627997	0 34 40 42 46 54 64 76 90 102 112 120 124 126 132 166	-1423178550670
STPT(10)	2234264422327168277	0 2 54 56 72 74 90 92 144 146	-1036469010390
SPT(16)	2234264661563409707	0 24 50 74 86 170 192 200 246 254 276 360 372 396 422 446	-797232768960
SPT(16)	2234264989910898169	0 30 42 52 54 64 82 120 142 180 198 208 210 220 232 262	-468885280498
STPT(10)	2234265324711280319	0 2 18 20 30 32 42 44 60 62	-134084898348
SPT(16)	2234265466759826333	0 18 36 44 54 56 78 80 114 116 138 140 150 158 176 194	7963647666
SPT(16)	2234265543430301089	0 4 34 102 132 148 174 198 244 268 294 310 340 408 438 442	84634122422
SPT(16)	2234265875375692793	0 50 66 108 116 164 174 206 228 260 270 318 326 368 384 434	416579514126
SPT(16)	2234266086000004741	0 12 18 28 42 126 130 132 166 168 172 256 270 280 286 298	627203826074
SPT(15)	2234266100941955999	0 24 84 150 162 234 252 282 312 330 402 414 480 540 564	642145777332