Prime p₀= 4364177789938313537 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 82 2 28 2 34 2 28 2 82 2 (?)
a_n: 0 2 84 86 114 116 150 152 180 182 264 266
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: 266
Found by: Autofuzzy
db: batch=85, k=12, 2 82 2 28 2 34

STPT(10)	4364176618071191819	0 2 18 20 30 32 42 44 60 62	-1171867121718
SPT(16)	4364176843689073129	0 28 34 42 54 70 102 118 144 160 192 208 220 228 234 262	-946249240408
SPT(16)	4364177179159848709	0 42 52 70 102 120 130 138 154 162 172 190 222 240 250 292	-610778464828
SPT(16)	4364177513090887861	0 6 12 42 52 90 96 102 160 166 172 210 220 250 256 262	-276847425676
SPT(18)	4364177513707979689	0 28 42 54 64 88 130 142 144 208 210 222 264 288 298 310 324 352	-276230333848
STPT(10)	4364177550347147129	0 2 42 44 60 62 78 80 120 122	-239591166408
SPT(16)	4364178148502150903	0 26 80 126 138 176 224 246 338 360 408 446 458 504 558 584	358563837366
TPT(14)	4364178486353055659	0 2 42 44 48 50 78 80 120 122 132 134 168 170	696414742122
SPT(16)	4364178517101457363	0 24 30 36 46 58 60 64 150 154 156 168 178 184 190 214	727163143826
SPT(16)	4364178616741423621	0 16 36 42 60 82 126 130 138 142 186 208 226 232 252 268	826803110084
STPT(10)	4364178929531321777	0 2 30 32 60 62 90 92 120 122	1139593008240