Prime p₀= 257954167836613271 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 10 2 58 2 46 2 40 2 (?)
a_n: 0 2 6 8 18 20 78 80 126 128 168 170
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: 170
Found by: scrap
db: batch=69, k=12, 4 10 58 46 40

TPT(12)	257954102817630467	0 2 84 86 162 164 204 206 210 212 222 224	-65018982804
SPT(14)	257954124712105121	0 60 80 122 126 150 192 200 242 266 270 312 332 392	-43124508150
SPT(14)	257954128531715939	0 60 72 98 140 144 180 182 218 222 264 290 302 362	-39304897332
SPT(14)	257954134570157887	0 12 16 42 52 54 60 136 142 144 154 180 184 196	-33266455384
SPT(14)	257954146126698677	0 56 66 74 84 96 132 194 230 242 252 260 270 326	-21709914594
SPT(14)	257954166912556273	0 24 70 106 108 136 174 190 228 256 258 294 340 364	-924056998
SPT(14)	257954172516514637	0 14 44 80 116 144 150 176 182 210 246 282 312 326	4679901366
TPT(12)	257954174585912687	0 2 42 44 120 122 150 152 192 194 210 212	6749299416
SPT(14)	257954184656353279	0 24 34 54 78 90 112 120 142 154 178 198 208 232	16819740008
SPT(14)	257954195291182043	0 24 30 38 54 86 96 98 108 140 156 164 170 194	27454568772
SPT(14)	257954209372982377	0 10 24 34 52 82 90 154 162 192 210 220 234 244	41536369106