Prime p₀= 2342353219210743227 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 64 2 70 2 10 2 28 2 (?)
a_n: 0 2 24 26 84 86 150 152 222 224 234 236 264 266
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: 266
Found by: Landjunge
db: batch=81, k=14, 22 58 64 70 10 28

SPT(16)	2342351894745827417	0 14 32 36 120 146 194 222 224 252 300 326 410 414 432 446	-1324464915810
SPT(16)	2342352641701938499	0 18 88 112 130 154 190 204 208 222 258 282 300 324 394 412	-577508804728
SPT(16)	2342352706300007981	0 6 32 42 90 108 110 152 186 228 230 248 296 306 332 338	-512910735246
STPT(10)	2342352710171731637	0 2 30 32 120 122 210 212 240 242	-509039011590
STPT(10)	2342352855780601397	0 2 30 32 42 44 54 56 84 86	-363430141830
SPT(16)	2342352941433766463	0 20 24 30 48 90 96 108 146 158 164 206 224 230 234 254	-277776976764
SPT(16)	2342354227976688721	0 6 12 90 108 130 132 136 252 256 258 280 298 376 382 388	1008765945494
STPT(10)	2342354363302860131	0 2 36 38 78 80 120 122 156 158	1144092116904
SPT(16)	2342354712614067169	0 72 88 124 130 142 144 148 204 208 210 222 228 264 280 352	1493403323942
SPT(16)	2342354918917583501	0 122 128 156 176 206 218 228 350 360 372 402 422 450 456 578	1699706840274
STPT(10)	2342355451864942901	0 2 78 80 168 170 258 260 336 338	2232654199674