Prime p₀= 1268551460110190747 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 16 2 22 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 54 56 72 74 84 86
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: 86
Found by: Megacruncher
db: batch=77, k=12, 2 10 2 16 2 22

SPT(16)	1268550668576933639	0 30 44 104 132 134 162 170 174 182 210 212 240 300 314 344	-791533257108
STPT(10)	1268550734021943257	0 2 12 14 42 44 72 74 84 86	-726088247490
SPT(16)	1268550745263533863	0 24 36 40 54 120 138 196 228 286 304 370 384 388 400 424	-714846656884
STPT(10)	1268551277340156779	0 2 12 14 30 32 48 50 60 62	-182770033968
SPT(16)	1268551278635032309	0 4 22 82 114 142 154 168 334 348 360 388 420 480 498 502	-181475158438
STPT(10)	1268551310732617907	0 2 30 32 72 74 114 116 144 146	-149377572840
SPT(16)	1268551683822499379	0 2 42 44 174 252 294 338 354 398 440 518 648 650 690 692	223712308632
SPT(16)	1268551767573843847	0 12 30 42 70 94 136 156 160 180 222 246 274 286 304 316	307463653100
SPT(16)	1268551854155410399	0 28 60 130 168 190 222 238 264 280 312 334 372 442 474 502	394045219652
SPT(16)	1268551898933507819	0 24 42 72 78 92 120 134 228 242 270 284 290 320 338 362	438823317072
STPT(10)	1268551915536109049	0 2 18 20 30 32 42 44 60 62	455425918302