Prime p₀= 999252277255612769 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 70 2 58 2 4 2 58 2 70 2 (?)
a_n: 0 2 72 74 132 134 138 140 198 200 270 272
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: 272
Found by: stoneageman
db: batch=76, k=12, 2 70 2 58 2 4

SPT(16)	999250924773788123	0 20 38 48 68 78 84 104 114 134 140 150 170 180 198 218	-1352481824646
STPT(10)	999251395689358937	0 2 30 32 72 74 114 116 144 146	-881566253832
STPT(10)	999251397995742887	0 2 30 32 72 74 114 116 144 146	-879259869882
SPT(16)	999251641083708277	0 30 42 46 90 126 150 156 196 202 226 262 306 310 322 352	-636171904492
SPT(18)	999251650968741251	0 20 26 48 92 120 146 222 230 258 266 342 368 396 440 462 468 488	-626286871518
STPT(10)	999251708470833047	0 2 24 26 42 44 60 62 84 86	-568784779722
SPT(16)	999252404843897921	0 6 96 120 126 140 150 156 230 236 246 260 266 290 380 386	127588285152
SPT(16)	999252473374115641	0 6 18 28 30 52 70 88 90 108 126 148 150 160 172 178	196118502872
STPT(12)	999252483337078937	0 2 30 32 114 116 150 152 234 236 264 266	206081466168
STPT(10)	999252920024697797	0 2 30 32 42 44 54 56 84 86	642769085028
STPT(12)	999253310944825751	0 2 36 38 48 50 78 80 90 92 126 128	1033689212982