Prime p₀= 383161353988916297 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 226 2 22 2 58 2 58 2 (?)
a_n: 0 2 12 14 240 242 264 266 324 326 384 386
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: 386
Found by: Cruncher Pete
db: batch=70, k=12, 10 226 22 58 58

SPT(15)	383161275391770383	0 30 114 120 126 186 204 270 336 354 414 420 426 510 540	-78597145914
SPT(14)	383161278511338053	0 68 80 96 114 168 194 240 266 320 338 354 366 434	-75477578244
SPT(14)	383161300776128257	0 36 42 102 120 126 132 160 166 172 190 250 256 292	-53212788040
SPT(14)	383161312982657707	0 16 40 46 82 102 106 120 124 144 180 186 210 226	-41006258590
SPT(14)	383161332353008439	0 2 20 38 80 104 114 158 168 192 234 252 270 272	-21635907858
SPT(14)	383161349208518239	0 28 64 72 90 94 118 144 168 172 190 198 234 262	-4780398058
SPT(14)	383161368419320081	0 6 10 12 28 40 70 78 108 120 136 138 142 148	14430403784
SPT(14)	383161369644421897	0 6 16 22 34 42 46 60 64 72 84 90 100 106	15655505600
SPT(14)	383161396272066799	0 10 24 48 90 100 114 154 168 178 220 244 258 268	42283150502
SPT(16)	383161425890488849	0 28 30 42 48 58 90 118 234 262 294 304 310 322 324 352	71901572552
SPT(14)	383161427054122811	0 12 20 98 108 110 138 182 210 212 222 300 308 320	73065206514