Prime p₀= 2123425308867647429 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: [SG-2W]Kurzer
db: batch=80, k=12, 2 10 2 58 2 4

SPT(16)	2123423565861670333	0 10 24 46 78 88 108 144 160 196 216 226 258 280 294 304	-1743005977096
STPT(10)	2123424140818383827	0 2 30 32 72 74 114 116 144 146	-1168049263602
SPT(16)	2123424213423826297	0 34 46 54 66 84 90 96 124 130 136 154 166 174 186 220	-1095443821132
STPT(10)	2123424254747993339	0 2 18 20 30 32 42 44 60 62	-1054119654090
SPT(16)	2123424259890718297	0 52 76 84 94 142 156 162 184 190 204 252 262 270 294 346	-1048976929132
SPT(16)	2123425123117759561	0 16 18 58 72 88 100 106 192 198 210 226 240 280 282 298	-185749887868
SPT(16)	2123425489675402519	0 22 34 54 60 124 144 204 220 280 300 364 370 390 402 424	180807755090
STPT(10)	2123425506340748609	0 2 18 20 30 32 42 44 60 62	197473101180
STPT(10)	2123425988938573127	0 2 30 32 42 44 54 56 84 86	680070925698
SPT(16)	2123426172028394171	0 12 72 78 102 116 120 180 368 428 432 446 470 476 536 548	863160746742
SPT(16)	2123426295804438433	0 58 76 84 124 144 190 216 238 264 310 330 370 378 396 454	986936791004