Prime p₀= 2319256594023879359 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 4 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 48 50 78 80 90 92
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: 92
Found by: Orange Kid
db: batch=81, k=12, 2 10 2 28 2 4

SPT(16)	2319255662499972929	0 12 24 68 78 80 90 104 168 182 192 194 204 248 260 272	-931523906430
STPT(10)	2319255894279882821	0 2 6 8 48 50 90 92 96 98	-699743996538
STPT(10)	2319256291177568777	0 2 60 62 72 74 84 86 144 146	-302846310582
STPT(10)	2319256297464163877	0 2 30 32 42 44 54 56 84 86	-296559715482
SPT(16)	2319256418718657503	0 18 26 96 140 150 170 210 224 264 284 294 338 408 416 434	-175305221856
STPT(10)	2319256453245977657	0 2 24 26 42 44 60 62 84 86	-140777901702
SPT(16)	2319256655802628247	0 26 32 44 62 116 132 140 156 164 180 234 252 264 270 296	61778748888
SPT(16)	2319256913025949661	0 30 42 50 120 140 156 162 290 296 312 332 402 410 422 452	319002070302
SPT(16)	2319256955990889751	0 22 30 70 126 132 156 160 168 172 196 202 258 298 306 328	361967010392
SPT(16)	2319256988974798669	0 12 54 114 118 132 144 150 202 208 220 234 238 298 340 352	394950919310
STPT(10)	2319257245129997111	0 2 36 38 78 80 120 122 156 158	651106117752