Prime p₀= 1120082135768435027 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 22 2 16 2 178 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 222 224 240 242 264 266
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: 266
Found by: Daniel
db: batch=76, k=12, 2 22 2 16 2 178

SPT(16)	1120080797384242579	0 12 28 42 48 88 90 118 264 292 294 334 340 354 370 382	-1338384192448
STPT(10)	1120080866340423341	0 2 6 8 48 50 90 92 96 98	-1269428011686
SPT(16)	1120081422621452111	0 62 80 98 108 150 212 228 272 288 350 392 402 420 438 500	-713146982916
TPT(14)	1120081630464474479	0 2 18 20 42 44 60 62 90 92 138 140 180 182	-505303960548
SPT(16)	1120081713377425091	0 18 38 62 140 156 182 192 206 216 242 258 336 360 380 398	-422391009936
TPT(14)	1120081822830667181	0 2 90 92 156 158 216 218 270 272 288 290 336 338	-312937767846
STPT(10)	1120082188707506597	0 2 24 26 42 44 60 62 84 86	52939071570
SPT(16)	1120082479913906783	0 14 18 24 60 66 108 128 156 176 218 224 260 266 270 284	344145471756
STPT(10)	1120082534747624351	0 2 36 38 78 80 120 122 156 158	398979189324
SPT(16)	1120082649587024111	0 20 30 42 62 80 146 150 182 186 252 270 290 302 312 332	513818589084
SPT(16)	1120082788947812147	0 14 20 42 80 84 90 104 132 146 152 156 194 216 222 236	653179377120