Prime p₀= 1267564492295017997 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 10 2 64 2 10 2 40 2 (?)
a_n: 0 2 42 44 54 56 120 122 132 134 174 176
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: 176
Found by: biodoc
db: batch=77, k=12, 2 40 2 10 2 64

SPT(16)	1267563197895280549	0 28 58 72 102 132 268 310 312 354 490 520 550 564 594 622	-1294399737448
STPT(10)	1267563332852310581	0 2 6 8 48 50 90 92 96 98	-1159442707416
SPT(16)	1267563490469224759	0 70 82 90 100 108 160 172 180 192 244 252 262 270 282 352	-1001825793238
SPT(16)	1267563513757170037	0 22 24 36 42 52 90 94 102 106 144 154 160 172 174 196	-978537847960
TPT(14)	1267564060207685561	0 2 66 68 126 128 138 140 180 182 270 272 276 278	-432087332436
STPT(10)	1267564386145649489	0 2 18 20 30 32 42 44 60 62	-106149368508
SPT(16)	1267564525167362273	0 8 20 26 66 90 134 140 144 150 194 218 258 264 276 284	32872344276
SPT(16)	1267564655292416539	0 24 34 48 94 102 108 174 238 304 310 318 364 378 388 412	162997398542
STPT(10)	1267564803086711807	0 2 12 14 42 44 72 74 84 86	310791693810
STPT(10)	1267564937132415587	0 2 30 32 42 44 54 56 84 86	444837397590
SPT(16)	1267565811283028707	0 10 36 52 84 94 112 132 274 294 312 322 354 370 396 406	1318988010710