Prime p₀= 167126328478293101 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 40 2 28 2 40 2 16 2 (?)
a_n: 0 2 36 38 78 80 108 110 150 152 168 170
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: emoga
db: batch=67, k=12, 34 40 28 40 16

SPT(14)	167126271827393311	0 12 30 46 72 96 102 196 202 226 252 268 286 298	-56650899790
SPT(14)	167126283647826337	0 6 30 70 72 84 94 132 142 154 156 196 220 226	-44830466764
SPT(14)	167126283848392567	0 6 30 46 130 144 156 184 196 210 294 310 334 340	-44629900534
SPT(14)	167126300394118669	0 48 60 108 120 130 162 370 402 412 424 472 484 532	-28084174432
TPT(12)	167126314248803801	0 2 6 8 48 50 78 80 108 110 126 128	-14229489300
SPT(14)	167126322491714669	0 2 30 48 80 90 108 122 140 150 182 200 228 230	-5986578432
SPT(14)	167126329241811749	0 14 62 80 90 104 108 164 168 182 192 210 258 272	763518648
SPT(14)	167126330212313191	0 48 88 90 100 102 108 202 208 210 220 222 262 310	1734020090
SPT(14)	167126350851106081	0 30 100 166 178 196 210 238 252 270 282 348 418 448	22372812980
SPT(14)	167126353280648479	0 18 28 34 48 60 84 124 148 160 174 180 190 208	24802355378
SPT(14)	167126379341913653	0 6 26 98 104 116 138 176 198 210 216 288 308 314	50863620552