Prime p₀= 131499176426455889 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 22 2 16 2 16 2 40 2 (?)
a_n: 0 2 18 20 42 44 60 62 78 80 120 122
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: 122
Found by: [SG]ATA-Rolf
db: batch=67, k=12, 16 22 16 16 40

SPT(14)	131499090978374641	0 22 36 42 78 88 90 118 120 130 166 172 186 208	-85448081248
SPT(14)	131499109279496561	0 42 80 96 110 180 206 252 278 348 362 378 416 458	-67146959328
SPT(14)	131499120143973299	0 2 72 78 90 102 144 158 200 212 224 230 300 302	-56282482590
SPT(14)	131499158857143929	0 8 78 90 92 140 158 192 210 258 260 272 342 350	-17569311960
TPT(12)	131499159952817297	0 2 84 86 102 104 114 116 264 266 312 314	-16473638592
SPT(14)	131499163403267369	0 12 24 50 110 120 132 140 152 162 222 248 260 272	-13023188520
SPT(14)	131499176515006439	0 14 24 74 90 122 128 144 150 182 198 248 258 272	88550550
SPT(14)	131499182037356317	0 34 52 60 84 94 144 160 210 220 244 252 270 304	5610900428
SPT(14)	131499203581029281	0 8 12 48 50 72 90 140 158 180 182 218 222 230	27154573392
SPT(14)	131499211075636267	0 12 22 36 40 42 76 120 154 156 160 174 184 196	34649180378
SPT(14)	131499232955047799	0 24 62 92 122 158 168 374 384 420 450 480 518 542	56528591910