Prime p₀= 261527685346249031 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 64 2 142 2 4 2 100 2 28 2 (?)
a_n: 0 2 66 68 210 212 216 218 318 320 348 350
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: 350
Found by: Roadranner
db: batch=69, k=12, 64 142 4 100 28

SPT(14)	261527558289498073	0 28 100 118 124 138 160 174 196 210 216 234 306 334	-127056750958
SPT(14)	261527604167903551	0 46 66 130 142 178 192 196 210 246 258 322 342 388	-81178345480
SPT(14)	261527667267999061	0 12 52 66 88 100 108 130 138 150 172 186 226 238	-18078249970
SPT(14)	261527670859850033	0 14 18 38 78 80 114 254 288 290 330 350 354 368	-14486398998
SPT(14)	261527671302341617	0 4 82 94 132 150 154 192 196 214 252 264 342 346	-14043907414
SPT(14)	261527671769446441	0 46 76 90 100 102 106 126 130 132 142 156 186 232	-13576802590
SPT(14)	261527717134697119	0 42 60 72 94 138 144 178 184 228 250 262 280 322	31788448088
TPT(12)	261527726101869167	0 2 24 26 54 56 90 92 120 122 150 152	40755620136
SPT(20)	261527729529607837	0 22 36 66 70 76 114 162 190 216 220 246 274 322 360 366 370 400 414 436	44183358806
TPT(12)	261527773768968701	0 2 36 38 78 80 96 98 156 158 168 170	88422719670
TPT(12)	261527778552583721	0 2 6 8 36 38 78 80 90 92 138 140	93206334690