Prime p₀= 1268561767131720989 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 16 2 40 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 72 74 90 92 102 104
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: 104
Found by: Megacruncher
db: batch=77, k=12, 2 10 2 16 2 40

STPT(10)	1268559894339804257	0 2 42 44 72 74 102 104 144 146	-1872791916732
SPT(16)	1268560061357525609	0 8 30 54 110 134 170 210 212 252 288 312 368 392 414 422	-1705774195380
SPT(16)	1268560162557754793	0 20 38 84 90 158 180 206 258 284 306 374 380 426 444 464	-1604573966196
SPT(16)	1268560630303039309	0 4 22 54 70 82 84 118 264 298 300 312 328 360 378 382	-1136828681680
STPT(10)	1268560852971250721	0 2 36 38 78 80 120 122 156 158	-914160470268
SPT(16)	1268561142788504911	0 10 12 48 106 126 132 150 178 196 202 222 280 316 318 328	-624343216078
STPT(10)	1268562484143211247	0 2 12 14 42 44 72 74 84 86	717011490258
SPT(16)	1268562542688574823	0 26 54 104 128 180 204 216 218 230 254 306 330 380 408 434	775556853834
SPT(16)	1268562910192947847	0 30 66 90 102 136 150 162 184 196 210 244 256 280 316 346	1143061226858
STPT(10)	1268562978567064001	0 2 6 8 48 50 90 92 96 98	1211435343012
STPT(10)	1268563087322100539	0 2 12 14 30 32 48 50 60 62	1320190379550