Prime p₀= 1122865070726039567 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 52 2 34 2 82 2 34 2 52 2 (?)
a_n: 0 2 54 56 90 92 174 176 210 212 264 266
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: crashtech
db: batch=76, k=12, 2 52 2 34 2 82

SPT(16)	1122864460653037387	0 22 64 76 82 94 96 120 136 160 162 174 180 192 234 256	-610073002180
SPT(16)	1122864621014008447	0 12 66 94 102 150 172 196 210 234 256 304 312 340 394 406	-449712031120
STPT(10)	1122864624980215847	0 2 30 32 72 74 114 116 144 146	-445745823720
SPT(16)	1122864648802965317	0 6 14 30 44 54 90 96 104 110 146 156 170 186 194 200	-421923074250
STPT(10)	1122864940621580657	0 2 12 14 72 74 132 134 144 146	-130104458910
SPT(16)	1122864949708393079	0 12 114 122 128 168 180 192 200 212 224 264 270 278 380 392	-121017646488
SPT(16)	1122865500023662697	0 24 26 42 66 96 110 122 144 156 170 200 224 240 242 266	429297623130
STPT(10)	1122865560897153257	0 2 30 32 60 62 90 92 120 122	490171113690
STPT(10)	1122865910946969179	0 2 48 50 90 92 132 134 180 182	840220929612
SPT(16)	1122866188540244177	0 30 56 80 120 150 152 162 200 210 212 242 282 306 332 362	1117814204610
STPT(10)	1122866286869088401	0 2 6 8 48 50 90 92 96 98	1216143048834