Prime p₀= 2566769009121782669 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: JayPi
db: batch=82, k=12, 2 10 2 58 2 4

STPT(12)	2566767655892067347	0 2 12 14 24 26 30 32 42 44 54 56	-1353229715322
SPT(16)	2566767802220280787	0 36 90 102 120 154 160 172 174 186 192 226 244 256 310 346	-1206901501882
STPT(10)	2566768624416468089	0 2 48 50 60 62 72 74 120 122	-384705314580
STPT(10)	2566768757496294191	0 2 36 38 78 80 120 122 156 158	-251625488478
SPT(16)	2566768922261374763	0 20 36 48 84 86 104 126 128 150 168 170 206 218 234 254	-86860407906
SPT(16)	2566768965732929537	0 60 62 72 104 110 144 156 170 182 216 222 254 264 266 326	-43388853132
SPT(16)	2566769028328208471	0 48 62 66 92 126 138 180 188 230 242 276 302 306 320 368	19206425802
STPT(10)	2566769303405191499	0 2 18 20 30 32 42 44 60 62	294283408830
SPT(16)	2566769681947367021	0 42 48 90 108 138 140 182 198 240 242 272 290 332 338 380	672825584352
SPT(16)	2566769919035736721	0 40 42 72 82 108 112 130 150 168 172 198 208 238 240 280	909913954052
SPT(16)	2566769972754759097	0 30 36 72 82 100 112 126 196 210 222 240 250 286 292 322	963632976428