Prime p₀= 199961440279146779 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 28 2 28 2 (?)
a_n: 0 2 60 62 72 74 102 104 132 134 162 164
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: 164
Found by: desktop64
db: batch=69, k=12, 58 10 28 28 28

SPT(16)	199961387690631407	0 60 66 150 162 164 176 180 206 210 222 224 236 320 326 386	-52588515372
SPT(14)	199961388385759541	0 2 48 146 150 170 192 266 288 308 312 410 456 458	-51893387238
SPT(14)	199961400245404999	0 22 78 130 144 148 154 168 174 178 192 244 300 322	-40033741780
TPT(12)	199961402855967251	0 2 30 32 78 80 90 92 120 122 156 158	-37423179528
TPT(12)	199961424183256511	0 2 96 98 270 272 318 320 378 380 408 410	-16095890268
SPT(14)	199961433232371631	0 6 28 46 52 60 88 90 118 126 132 150 172 178	-7046775148
TPT(12)	199961454143402519	0 2 138 140 150 152 162 164 240 242 252 254	13864255740
SPT(14)	199961454360840539	0 24 42 48 92 98 134 138 174 180 224 230 248 272	14081693760
TPT(12)	199961462153377217	0 2 42 44 60 62 144 146 192 194 210 212	21874230438
TPT(12)	199961473643542139	0 2 12 14 90 92 222 224 240 242 258 260	33364395360
SPT(14)	199961501666893279	0 10 40 48 52 54 78 124 148 150 154 162 192 202	61387746500