Prime p₀= 3015883942720449137 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 178 2 16 2 28 2 76 2 10 2 (?)
a_n: 0 2 54 56 234 236 252 254 282 284 360 362 372 374
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: 374
Found by: ginga
db: batch=82, k=14, 52 178 16 28 76 10

SPT(16)	3015880469211109823	0 8 24 66 110 134 140 164 240 264 270 294 338 380 396 404	-3473509339314
SPT(16)	3015881646368008609	0 42 64 70 78 88 90 112 120 142 144 154 162 168 190 232	-2296352440528
STPT(10)	3015882001770486419	0 2 18 20 30 32 42 44 60 62	-1940949962718
STPT(10)	3015882679322209727	0 2 30 32 60 62 90 92 120 122	-1263398239410
SPT(16)	3015882768902372431	0 10 30 46 130 132 156 166 186 196 220 222 306 322 342 352	-1173818076706
TPT(14)	3015883218376601471	0 2 6 8 108 110 150 152 216 218 246 248 306 308	-724343847666
STPT(10)	3015884263784146121	0 2 6 8 48 50 90 92 96 98	321063696984
TPT(14)	3015884321703308831	0 2 18 20 96 98 150 152 156 158 198 200 276 278	378982859694
SPT(16)	3015884848256471501	0 30 38 48 78 98 120 128 162 170 192 212 242 252 260 290	905536022364
STPT(10)	3015884881347105569	0 2 42 44 90 92 138 140 180 182	938626656432
SPT(16)	3015885119313438181	0 12 40 60 106 150 162 168 190 196 208 252 298 318 346 358	1176592989044