Prime p₀= 1120926420957488051 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 58 2 4 2 58 2 28 2 (?)
a_n: 0 2 30 32 90 92 96 98 156 158 186 188
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: 188
Found by: vinn@[CNT]
db: batch=76, k=12, 2 28 2 58 2 4

SPT(16)	1120925941583823461	0 6 8 38 66 78 116 140 168 192 230 242 270 300 302 308	-479373664590
STPT(10)	1120925949391333871	0 2 30 32 60 62 90 92 120 122	-471566154180
STPT(10)	1120926001501095149	0 2 42 44 90 92 138 140 180 182	-419456392902
SPT(16)	1120926059722648453	0 4 28 54 58 60 70 88 96 114 124 126 130 156 180 184	-361234839598
SPT(16)	1120926196975401787	0 22 24 34 40 90 106 112 144 150 166 216 222 232 234 256	-223982086264
STPT(10)	1120926239755169537	0 2 30 32 42 44 54 56 84 86	-181202318514
SPT(16)	1120926513250357763	0 60 120 126 200 224 230 306 314 390 396 420 494 500 560 620	92292869712
STPT(10)	1120926569408916209	0 2 18 20 30 32 42 44 60 62	148451428158
TPT(14)	1120927474674728801	0 2 78 80 90 92 216 218 246 248 276 278 300 302	1053717240750
TPT(14)	1120927630915444787	0 2 42 44 54 56 114 116 162 164 204 206 372 374	1209957956736
STPT(10)	1120927766618834219	0 2 48 50 90 92 132 134 180 182	1345661346168