Prime p₀= 567538694782826357 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 130 2 46 2 10 2 28 2 40 2 (?)
a_n: 0 2 132 134 180 182 192 194 222 224 264 266
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: 266
Found by: nenym
db: batch=71, k=12, 130 46 10 28 40

SPT(14)	567538634673644129	0 12 48 80 122 152 168 254 270 300 342 374 410 422	-60109182228
SPT(14)	567538637419699097	0 12 26 116 132 146 152 174 180 194 210 300 314 326	-57363127260
SPT(14)	567538638685333877	0 2 42 44 50 60 84 92 116 126 132 134 174 176	-56097492480
SPT(14)	567538640875915169	0 32 42 80 114 168 194 198 224 278 312 350 360 392	-53906911188
SPT(14)	567538664693900041	0 28 58 60 70 72 90 130 148 150 160 162 192 220	-30088926316
SPT(14)	567538675557014303	0 38 48 90 140 164 198 260 294 318 368 410 420 458	-19225812054
TPT(12)	567538697104300217	0 2 30 32 72 74 84 86 114 116 270 272	2321473860
SPT(14)	567538702598204693	0 14 24 44 54 56 80 90 114 116 126 146 156 170	7815378336
SPT(14)	567538730494139851	0 52 66 82 88 132 166 222 256 300 306 322 336 388	35711313494
SPT(14)	567538736662054021	0 18 40 60 76 78 90 118 130 132 148 168 190 208	41879227664
TPT(12)	567538740460211951	0 2 30 32 156 158 186 188 198 200 210 212	45677385594