Prime p₀= 567538697104300217 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 40 2 10 2 28 2 154 2 (?)
a_n: 0 2 30 32 72 74 84 86 114 116 270 272
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: 272
Found by: nenym
db: batch=71, k=12, 28 40 10 28 154

SPT(14)	567538637419699097	0 12 26 116 132 146 152 174 180 194 210 300 314 326	-59684601120
SPT(14)	567538638685333877	0 2 42 44 50 60 84 92 116 126 132 134 174 176	-58418966340
SPT(14)	567538640875915169	0 32 42 80 114 168 194 198 224 278 312 350 360 392	-56228385048
SPT(14)	567538664693900041	0 28 58 60 70 72 90 130 148 150 160 162 192 220	-32410400176
SPT(14)	567538675557014303	0 38 48 90 140 164 198 260 294 318 368 410 420 458	-21547285914
TPT(12)	567538694782826357	0 2 132 134 180 182 192 194 222 224 264 266	-2321473860
SPT(14)	567538702598204693	0 14 24 44 54 56 80 90 114 116 126 146 156 170	5493904476
SPT(14)	567538730494139851	0 52 66 82 88 132 166 222 256 300 306 322 336 388	33389839634
SPT(14)	567538736662054021	0 18 40 60 76 78 90 118 130 132 148 168 190 208	39557753804
TPT(12)	567538740460211951	0 2 30 32 156 158 186 188 198 200 210 212	43355911734
SPT(16)	567538745159202667	0 6 16 30 34 90 102 126 130 154 166 222 226 240 250 256	48054902450