Prime p₀= 2423367082179235319 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 58 2 4 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 78 80 138 140 150 152
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: 152
Found by: JayPi
db: batch=82, k=12, 2 10 2 58 2 4

TPT(14)	2423363352655008611	0 2 66 68 78 80 108 110 126 128 156 158 180 182	-3729524226708
SPT(16)	2423365234843504087	0 10 42 66 90 94 96 112 174 190 192 196 220 244 276 286	-1847335731232
SPT(16)	2423365749193285087	0 34 64 66 76 90 114 154 156 196 220 234 244 246 276 310	-1332985950232
STPT(10)	2423365819917085229	0 2 18 20 30 32 42 44 60 62	-1262262150090
STPT(10)	2423366477437784111	0 2 30 32 78 80 126 128 156 158	-604741451208
SPT(16)	2423366554419962023	0 10 36 46 78 94 130 228 256 354 390 406 438 448 474 484	-527759273296
SPT(16)	2423367410165639669	0 20 32 68 78 110 162 218 222 278 330 362 372 408 420 440	327986404350
SPT(16)	2423367549141906397	0 16 24 46 120 154 156 162 304 310 312 346 420 442 450 466	466962671078
STPT(10)	2423367609615764477	0 2 12 14 42 44 72 74 84 86	527436529158
SPT(16)	2423368065093966559	0 18 72 78 90 132 144 162 240 258 270 312 324 330 384 402	982914731240
STPT(10)	2423368201786534811	0 2 6 8 48 50 90 92 96 98	1119607299492