Prime p₀= 848238039954726467 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 40 2 4 2 40 2 10 2 (?)
a_n: 0 2 12 14 54 56 60 62 102 104 114 116
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: 116
Found by: Dr Who Fan
db: batch=73, k=12, 2 10 2 40 2 4

SPT(16)	848237241293382929	0 8 20 42 72 84 92 98 114 120 128 140 170 192 204 212	-798661343538
STPT(10)	848237277166901519	0 2 18 20 30 32 42 44 60 62	-762787824948
TPT(14)	848237475905465939	0 2 12 14 18 20 72 74 102 104 138 140 150 152	-564049260528
SPT(16)	848237947808312291	0 26 38 86 102 110 138 140 168 170 198 206 222 270 282 308	-92146414176
SPT(18)	848237976786276833	0 30 54 98 108 194 198 234 240 248 254 290 294 380 390 434 458 488	-63168449634
SPT(16)	848238004334374021	0 16 18 78 82 88 166 238 240 312 390 396 400 460 462 478	-35620352446
STPT(10)	848238582830369711	0 2 30 32 78 80 126 128 156 158	542875643244
STPT(12)	848238737879453909	0 2 30 32 60 62 102 104 132 134 162 164	697924727442
STPT(10)	848238797073222857	0 2 30 32 42 44 54 56 84 86	757118496390
STPT(10)	848238880551678557	0 2 30 32 42 44 54 56 84 86	840596952090
STPT(10)	848239210594275551	0 2 6 8 18 20 30 32 36 38	1170639549084