Prime p₀= 796324010343910931 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 178 2 10 2 46 2 52 2 118 2 (?)
a_n: 0 2 126 128 306 308 318 320 366 368 420 422 540 542
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: 542
Found by: Theadalus
db: batch=73, k=14, 124 178 10 46 52 118

SPT(16)	796322517127306219	0 10 18 42 52 70 94 130 162 198 222 240 250 274 282 292	-1493216604712
STPT(10)	796322539947419057	0 2 24 26 42 44 60 62 84 86	-1470396491874
STPT(10)	796322764626460829	0 2 18 20 30 32 42 44 60 62	-1245717450102
STPT(10)	796323119344394867	0 2 30 32 120 122 210 212 240 242	-890999516064
SPT(16)	796323322552529887	0 10 12 30 40 96 100 150 166 216 220 276 286 304 306 316	-687791381044
SPT(16)	796323380594642477	0 30 62 114 122 146 152 162 224 234 240 264 272 324 356 386	-629749268454
SPT(16)	796324751890455479	0 14 54 80 90 104 108 150 182 224 228 242 252 278 318 332	741546544548
STPT(10)	796325116546105919	0 2 12 14 90 92 168 170 180 182	1106202194988
STPT(10)	796325140810907471	0 2 30 32 78 80 126 128 156 158	1130466996540
SPT(16)	796325549253247549	0 30 48 82 84 138 160 184 228 252 274 328 330 364 382 412	1538909336618
STPT(10)	796325582637363587	0 2 30 32 42 44 54 56 84 86	1572293452656