Prime p₀= 391710584419317347 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 52 2 46 2 10 2 64 2 (?)
a_n: 0 2 60 62 114 116 162 164 174 176 240 242
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: 242
Found by: Cruncher Pete
db: batch=70, k=12, 58 52 46 10 64

SPT(14)	391710497360123699	0 42 60 108 120 150 164 168 182 212 224 272 290 332	-87059193648
SPT(14)	391710527876505191	0 6 8 50 72 78 90 98 110 116 138 180 182 188	-56542812156
SPT(14)	391710530668435889	0 18 42 50 78 80 120 140 180 182 210 218 242 260	-53750881458
SPT(14)	391710533574943201	0 6 100 136 156 160 168 190 198 202 222 258 352 358	-50844374146
SPT(14)	391710565181687933	0 30 44 56 86 110 156 194 240 264 294 306 320 350	-19237629414
SPT(16)	391710572060035031	0 12 56 60 66 72 86 102 110 126 140 146 152 156 200 212	-12359282316
SPT(14)	391710606896444491	0 6 82 132 166 186 216 292 322 342 376 426 502 508	22477127144
STPT(10)	391710718975310561	0 2 30 32 78 80 126 128 156 158	134555993214
SPT(14)	391710727466670721	0 18 28 42 118 130 172 186 228 240 316 330 340 358	143047353374
SPT(14)	391710728715324631	0 18 72 88 96 126 142 156 172 202 210 226 280 298	144296007284
SPT(14)	391710738804540709	0 78 94 100 120 130 154 264 288 298 318 324 340 418	154385223362