Prime p₀= 1091611056782768369 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 58 2 34 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 108 110 168 170 180 182
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: 182
Found by: [SG-2W]Kurzer
db: batch=76, k=12, 2 10 2 58 2 34

SPT(16)	1091610618776799049	0 12 42 54 64 112 120 130 144 154 162 210 220 232 262 274	-438005969320
STPT(10)	1091610681610390259	0 2 42 44 90 92 138 140 180 182	-375172378110
SPT(16)	1091610699276606473	0 6 74 90 108 116 144 156 158 170 198 206 224 240 308 314	-357506161896
STPT(10)	1091610716873667041	0 2 6 8 18 20 30 32 36 38	-339909101328
STPT(10)	1091610788415628841	0 2 6 8 48 50 90 92 96 98	-268367139528
STPT(10)	1091610987159943301	0 2 6 8 18 20 30 32 36 38	-69622825068
SPT(16)	1091611376047241521	0 10 40 52 70 76 90 96 112 118 132 138 156 168 198 208	319264473152
SPT(16)	1091611554379590263	0 24 108 140 164 174 200 206 288 294 320 330 354 386 470 494	497596821894
SPT(16)	1091611625905287611	0 26 62 78 80 126 180 230 378 428 482 528 530 546 582 608	569122519242
STPT(10)	1091611649340975179	0 2 18 20 30 32 42 44 60 62	592558206810
SPT(16)	1091611906766750717	0 32 60 66 96 110 122 126 200 204 216 230 260 266 294 326	849983982348