Prime p₀= 321168036206213237 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 10 2 148 2 46 2 40 2 (?)
a_n: 0 2 60 62 72 74 222 224 270 272 312 314
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: 314
Found by: marmot
db: batch=70, k=12, 58 10 148 46 40

SPT(14)	321167992979009413	0 28 96 108 118 150 168 268 286 318 328 340 408 436	-43227203824
SPT(14)	321167993585757119	0 2 8 42 72 74 128 174 228 230 260 294 300 302	-42620456118
TPT(12)	321167995129073039	0 2 78 80 138 140 162 164 180 182 210 212	-41077140198
SPT(14)	321168028306209397	0 36 40 42 60 82 96 136 150 172 190 192 196 232	-7900003840
SPT(14)	321168030381078893	0 6 20 56 96 110 140 150 180 194 234 270 284 290	-5825134344
SPT(14)	321168031174092233	0 24 36 50 80 98 228 266 396 414 444 458 470 494	-5032121004
TPT(12)	321168048991153319	0 2 48 50 60 62 180 182 258 260 312 314	12784940082
SPT(14)	321168049656998233	0 30 34 76 78 118 126 148 156 196 198 240 244 274	13450784996
STPT(10)	321168050981389277	0 2 30 32 42 44 54 56 84 86	14775176040
SPT(14)	321168086636948497	0 22 42 52 60 84 112 144 172 196 204 214 234 256	50430735260
SPT(14)	321168099573105311	0 36 50 62 80 98 108 140 150 168 186 198 212 248	63366892074