Prime p₀= 2397023073197359301 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 118 2 46 2 28 2 46 2 118 2 (?)
a_n: 0 2 120 122 168 170 198 200 246 248 366 368
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 368
Found by: [SG-2W]Kurzer
db: batch=81, k=12, 2 118 2 46 2 28

SPT(16)	2397021757645486471	0 42 66 100 112 142 190 232 240 282 330 360 372 406 430 472	-1315551872830
SPT(16)	2397022055711822237	0 2 12 26 44 66 110 116 150 156 200 222 240 254 264 266	-1017485537064
SPT(16)	2397022309959121067	0 60 66 72 104 110 144 146 150 152 186 192 224 230 236 296	-763238238234
TPT(14)	2397022648792299971	0 2 18 20 120 122 126 128 156 158 198 200 210 212	-424405059330
STPT(10)	2397022740211740437	0 2 30 32 42 44 54 56 84 86	-332985618864
SPT(16)	2397022967379038539	0 10 28 30 78 120 160 162 190 192 232 274 322 324 342 352	-105818320762
SPT(16)	2397023171790426961	0 46 52 70 82 136 250 292 300 342 456 510 522 540 546 592	98593067660
SPT(16)	2397023229514254389	0 2 14 20 72 80 114 140 174 200 234 242 294 300 312 314	156316895088
SPT(16)	2397023768335885837	0 40 82 84 142 144 150 186 220 256 262 264 322 324 366 406	695138526536
STPT(10)	2397023788264975349	0 2 18 20 30 32 42 44 60 62	715067616048
SPT(16)	2397023904737858827	0 124 156 216 256 264 300 324 382 406 442 450 490 550 582 706	831540499526