Prime p₀= 144467166346156991 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 4 2 40 2 28 2 88 2 (?)
a_n: 0 2 30 32 36 38 78 80 108 110 198 200
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: 200
Found by: emoga
db: batch=67, k=12, 28 4 40 28 88

SPT(16)	144467111844574759	0 10 30 70 94 100 114 130 132 148 162 168 192 232 252 262	-54501582232
SPT(14)	144467112323437609	0 10 52 88 90 102 142 168 208 220 222 258 300 310	-54022719382
SPT(14)	144467123288930669	0 12 90 152 164 182 194 210 222 240 252 314 392 404	-43057226322
SPT(14)	144467123810895209	0 48 74 78 98 140 150 158 168 210 230 234 260 308	-42535261782
SPT(14)	144467129618614597	0 22 72 90 100 114 126 160 172 186 196 214 264 286	-36727542394
SPT(14)	144467165665411157	0 30 56 72 92 116 176 210 270 294 314 330 356 386	-680745834
SPT(14)	144467174682704899	0 4 12 22 42 82 172 330 420 460 480 490 498 502	8336547908
STPT(10)	144467182487812697	0 2 42 44 102 104 162 164 204 206	16141655706
TPT(12)	144467201890290269	0 2 12 14 18 20 48 50 72 74 90 92	35544133278
SPT(14)	144467235428963761	0 6 70 90 96 100 118 150 168 172 178 198 262 268	69082806770
SPT(14)	144467269083849851	0 32 80 86 132 138 156 182 200 206 252 258 306 338	102737692860