Prime p₀= 378614949769680257 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 82 2 46 2 76 2 58 2 22 2 (?)
a_n: 0 2 84 86 132 134 210 212 270 272 294 296
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: 296
Found by: Cruncher Pete
db: batch=70, k=12, 82 46 76 58 22

SPT(14)	378614832981201301	0 16 30 78 88 136 150 196 210 258 268 316 330 346	-116788478956
STPT(10)	378614857027266941	0 2 6 8 48 50 90 92 96 98	-92742413316
SPT(14)	378614877924798313	0 10 36 60 88 106 130 144 168 186 214 238 264 274	-71844881944
TPT(12)	378614903699811587	0 2 12 14 30 32 54 56 84 86 90 92	-46069868670
SPT(14)	378614911617127681	0 16 48 60 70 90 108 118 136 156 166 178 210 226	-38152552576
SPT(14)	378614925478497167	0 20 56 66 80 116 120 206 210 246 260 270 306 326	-24291183090
SPT(14)	378614963546553779	0 24 30 38 42 44 114 188 258 260 264 272 278 302	13776873522
SPT(14)	378614963609086993	0 46 78 84 148 196 210 214 228 276 340 346 378 424	13839406736
SPT(14)	378614975380087739	0 12 20 24 132 150 182 222 254 272 380 384 392 404	25610407482
SPT(14)	378614985411897287	0 6 30 72 114 140 146 180 186 212 254 296 320 326	35642217030
TPT(12)	378615011764895747	0 2 72 74 90 92 174 176 210 212 240 242	61995215490