Prime p₀= 2928968273564120741 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 196 2 172 2 4 2 10 2 16 2 (?)
a_n: 0 2 48 50 246 248 420 422 426 428 438 440 456 458
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: 458
Found by: Landjunge
db: batch=82, k=14, 46 196 172 4 10 16

SPT(16)	2928966094947903733	0 6 48 66 76 78 84 90 94 100 106 108 118 136 178 184	-2178616217008
SPT(16)	2928967281920872397	0 14 20 50 60 102 134 162 182 210 242 284 294 324 330 344	-991643248344
SPT(16)	2928967375390123783	0 30 70 78 108 118 130 148 198 216 228 238 268 276 316 346	-898173996958
STPT(10)	2928967637798973467	0 2 12 14 72 74 132 134 144 146	-635765147274
SPT(16)	2928967655557301621	0 6 26 72 96 110 128 152 156 180 198 212 236 282 302 308	-618006819120
STPT(10)	2928967940860587959	0 2 12 14 90 92 168 170 180 182	-332703532782
STPT(10)	2928968347659482039	0 2 18 20 30 32 42 44 60 62	74095361298
SPT(16)	2928968881610056723	0 28 34 36 84 114 154 174 190 210 250 280 328 330 336 364	608045935982
STPT(10)	2928969047706296009	0 2 48 50 60 62 72 74 120 122	774142175268
STPT(10)	2928969062198799701	0 2 6 8 48 50 90 92 96 98	788634678960
SPT(16)	2928969786533632811	0 26 36 62 98 110 128 146 162 180 198 210 246 272 282 308	1512969512070