Prime p₀= 960392999666701427 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 40 2 124 2 40 2 10 2 (?)
a_n: 0 2 12 14 54 56 180 182 222 224 234 236
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: 236
Found by: Theadalus
db: batch=76, k=12, 2 10 2 40 2 124

SPT(16)	960391834652037119	0 12 44 122 132 150 170 182 222 234 254 272 282 360 392 404	-1165014664308
SPT(16)	960392025723919193	0 14 38 56 60 84 96 104 150 158 170 194 198 216 240 254	-973942782234
SPT(20)	960392346228466091	0 72 78 120 122 156 176 182 188 198 230 240 246 252 272 306 308 350 356 428	-653438235336
STPT(10)	960392385757155737	0 2 12 14 42 44 72 74 84 86	-613909545690
STPT(10)	960392646895664501	0 2 120 122 138 140 156 158 276 278	-352771036926
SPT(16)	960392993505517487	0 12 26 44 62 86 104 114 212 222 240 264 282 300 314 326	-6161183940
SPT(16)	960393635953479271	0 18 40 60 76 78 82 90 208 216 220 222 238 258 280 298	636286777844
STPT(10)	960393742936864679	0 2 42 44 60 62 78 80 120 122	743270163252
SPT(16)	960393761296534811	0 50 60 78 86 96 98 140 156 198 200 210 218 236 246 296	761629833384
TPT(14)	960393912122242397	0 2 42 44 60 62 72 74 114 116 132 134 174 176	912455540970
SPT(16)	960394084087895419	0 30 70 100 144 184 228 274 294 340 384 424 468 498 538 568	1084421193992