Prime p₀= 1126425441786669749 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 10 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 72 74 102 104 132 134
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: 134
Found by: crashtech
db: batch=76, k=12, 2 28 2 28 2 10

TPT(14)	1126424969191276367	0 2 30 32 42 44 60 62 72 74 90 92 114 116	-472595393382
SPT(16)	1126424979115102943	0 146 156 194 234 236 290 306 308 324 378 380 420 458 468 614	-462671566806
SPT(16)	1126425007939833773	0 8 44 66 86 90 108 120 134 146 164 168 188 210 246 254	-433846835976
STPT(10)	1126425107265327797	0 2 54 56 72 74 90 92 144 146	-334521341952
STPT(10)	1126425164556141629	0 2 12 14 90 92 168 170 180 182	-277230528120
SPT(16)	1126425216239998993	0 30 66 118 148 156 180 216 268 304 328 336 366 418 454 484	-225546670756
STPT(10)	1126425545600226257	0 2 12 14 42 44 72 74 84 86	103813556508
SPT(16)	1126426214230024447	0 4 36 54 70 106 120 166 210 256 270 306 322 340 372 376	772443354698
SPT(16)	1126426303146694993	0 4 10 46 48 66 70 76 78 84 88 106 108 144 150 154	861360025244
STPT(10)	1126426726234717517	0 2 30 32 42 44 54 56 84 86	1284448047768
TPT(14)	1126427364221229281	0 2 78 80 126 128 156 158 168 170 180 182 210 212	1922434559532