Prime p₀= 1016737583288753657 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 28 2 22 2 28 2 58 2 (?)
a_n: 0 2 60 62 90 92 114 116 144 146 204 206
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: 206
Found by: vinn@[CNT]
db: batch=76, k=12, 2 58 2 28 2 22

SPT(16)	1016736662704015807	0 10 12 16 22 114 126 180 196 250 262 354 360 364 366 376	-920584737850
SPT(18)	1016736777001242761	0 18 50 62 72 92 132 158 200 228 270 296 336 356 366 378 410 428	-806287510896
STPT(10)	1016737252710520037	0 2 30 32 72 74 114 116 144 146	-330578233620
SPT(16)	1016737397694937313	0 6 38 96 104 108 120 126 218 224 236 240 248 306 338 344	-185593816344
STPT(10)	1016737479042634199	0 2 42 44 90 92 138 140 180 182	-104246119458
TPT(14)	1016737583288753567	0 2 90 92 150 152 180 182 204 206 234 236 294 296	-90
STPT(10)	1016737808206265309	0 2 48 50 90 92 132 134 180 182	224917511652
SPT(16)	1016737974487657931	0 12 18 42 122 126 150 152 216 218 242 246 326 350 356 368	391198904274
STPT(10)	1016737986967945997	0 2 42 44 72 74 102 104 144 146	403679192340
STPT(10)	1016738144859422927	0 2 30 32 42 44 54 56 84 86	561570669270
STPT(10)	1016738249425540001	0 2 6 8 48 50 90 92 96 98	666136786344