Prime p₀= 2162497315183335287 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 22 2 28 2 64 2 28 2 22 2 (?)
a_n: 0 2 24 26 54 56 120 122 150 152 174 176
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: 176
Found by: Landjunge
db: batch=81, k=12, 2 22 2 28 2 64

SPT(16)	2162495539203712481	0 2 80 86 140 216 230 278 420 468 482 558 612 618 696 698	-1775979622806
STPT(10)	2162495563793915261	0 2 6 8 18 20 30 32 36 38	-1751389420026
SPT(16)	2162496268542893267	0 6 26 56 62 96 110 132 140 162 176 210 216 246 266 272	-1046640442020
STPT(10)	2162496837663961661	0 2 30 32 78 80 126 128 156 158	-477519373626
STPT(10)	2162496963478951919	0 2 78 80 120 122 162 164 240 242	-351704383368
STPT(10)	2162497177062116561	0 2 6 8 18 20 30 32 36 38	-138121218726
SPT(16)	2162497397373492241	0 46 90 96 118 186 208 222 286 300 322 390 412 418 462 508	82190156954
STPT(10)	2162497431974632301	0 2 6 8 48 50 90 92 96 98	116791297014
SPT(16)	2162497668541259653	0 10 36 58 60 66 118 148 156 186 238 244 246 268 294 304	353357924366
TPT(14)	2162497708269861419	0 2 78 80 132 134 162 164 210 212 228 230 270 272	393086526132
SPT(16)	2162498063722736917	0 22 52 60 72 130 162 204 220 262 294 352 364 372 402 424	748539401630