Prime p₀= 131381142707872691 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 106 2 28 2 46 2 178 2 (?)
a_n: 0 2 30 32 138 140 168 170 216 218 396 398
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: 398
Found by: [SG]ATA-Rolf
db: batch=67, k=12, 28 106 28 46 178

SPT(14)	131381052660976039	0 28 34 42 54 82 108 154 180 208 220 228 234 262	-90046896652
SPT(14)	131381071252374809	0 8 12 78 90 92 132 188 228 230 242 308 312 320	-71455497882
SPT(14)	131381101318016587	0 4 24 64 66 100 112 144 156 190 192 232 252 256	-41389856104
SPT(14)	131381111715468773	0 6 60 90 104 140 146 168 174 210 224 254 308 314	-30992403918
SPT(14)	131381111785534397	0 14 26 96 122 156 182 204 230 264 290 360 372 386	-30922338294
SPT(14)	131381127519564421	0 10 28 42 58 78 90 130 142 162 178 192 210 220	-15188308270
TPT(12)	131381146364233487	0 2 54 56 282 284 294 296 324 326 372 374	3656360796
SPT(14)	131381151370076563	0 36 46 76 96 114 120 124 130 148 168 198 208 244	8662203872
TPT(12)	131381169018589277	0 2 30 32 54 56 60 62 72 74 132 134	26310716586
SPT(14)	131381173945768463	0 30 68 80 140 150 168 176 194 204 264 276 314 344	31237895772
SPT(16)	131381176897277353	0 28 34 40 46 60 90 100 144 154 184 198 204 210 216 244	34189404662