Prime p₀= 1268545706937138239 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 10 2 64 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 108 110 120 122 150 152
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: Megacruncher
db: batch=77, k=12, 2 28 2 10 2 64

SPT(16)	1268544151737145991	0 56 68 78 92 116 126 138 140 152 162 186 200 210 222 278	-1555199992248
STPT(12)	1268544854416429097	0 2 30 32 60 62 72 74 102 104 132 134	-852520709142
TPT(14)	1268544854416429097	0 2 30 32 60 62 72 74 102 104 132 134 180 182	-852520709142
SPT(16)	1268544886351790039	0 12 38 90 98 128 158 180 200 222 252 282 290 342 368 380	-820585348200
SPT(16)	1268545173124567607	0 2 24 36 44 54 84 86 90 92 122 132 140 152 174 176	-533812570632
TPT(14)	1268545672388575367	0 2 12 14 24 26 42 44 54 56 132 134 330 332	-34548562872
STPT(10)	1268545884929864909	0 2 18 20 30 32 42 44 60 62	177992726670
SPT(16)	1268546036623052251	0 10 30 52 82 96 106 148 270 312 322 336 366 388 408 418	329685914012
TPT(14)	1268546200981570307	0 2 12 14 42 44 54 56 210 212 234 236 324 326	494044432068
STPT(10)	1268546280485770367	0 2 54 56 72 74 90 92 144 146	573548632128
TPT(14)	1268546679791365001	0 2 30 32 66 68 108 110 150 152 156 158 186 188	972854226762