Prime p₀= 1080737985757899617 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: stoneageman
db: batch=76, k=12, 2 10 2 10 2 4

SPT(16)	1080737480619290101	0 18 48 58 100 180 210 240 280 310 340 420 462 472 502 520	-505138609516
SPT(16)	1080737490993758281	0 6 46 90 112 132 190 210 238 258 316 336 358 402 442 448	-494764141336
SPT(16)	1080737502352751741	0 56 60 78 80 98 108 122 156 170 180 198 200 218 222 278	-483405147876
STPT(10)	1080737529134606009	0 2 18 20 30 32 42 44 60 62	-456623293608
SPT(16)	1080737827658050103	0 14 24 36 78 146 164 170 174 180 198 266 308 320 330 344	-158099849514
STPT(10)	1080737967059843537	0 2 90 92 132 134 174 176 264 266	-18698056080
SPT(16)	1080738130262427617	0 24 30 50 66 80 92 156 170 234 246 260 276 296 302 326	144504528000
STPT(10)	1080738173330545907	0 2 60 62 72 74 84 86 144 146	187572646290
STPT(10)	1080738250641428957	0 2 30 32 42 44 54 56 84 86	264883529340
SPT(16)	1080738632177909729	0 62 72 104 140 150 164 192 380 408 422 432 468 500 510 572	646420010112
STPT(10)	1080738668772590099	0 2 18 20 30 32 42 44 60 62	683014690482