Prime p₀= 87667405225477589 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 10 2 238 2 46 2 46 2 (?)
a_n: 0 2 30 32 42 44 282 284 330 332 378 380
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: 380
Found by: nenym
db: batch=67, k=12, 28 10 238 46 46

SPT(16)	87667338269931019	0 18 22 34 84 112 144 160 162 178 210 238 288 300 304 322	-66955546570
SPT(14)	87667340682566521	0 22 42 48 88 90 108 112 130 132 172 178 198 220	-64542911068
SPT(14)	87667347677742697	0 22 34 90 100 102 120 124 142 144 154 210 222 244	-57547734892
TPT(12)	87667370912524967	0 2 12 14 42 44 54 56 102 104 144 146	-34312952622
SPT(14)	87667392389638349	0 18 54 78 80 110 134 144 168 198 200 224 260 278	-12835839240
TPT(12)	87667401104739101	0 2 6 8 18 20 90 92 126 128 228 230	-4120738488
SPT(14)	87667423268944483	0 48 70 100 126 186 210 214 238 298 324 354 376 424	18043466894
TPT(12)	87667441121907329	0 2 18 20 60 62 72 74 102 104 132 134	35896429740
SPT(14)	87667444849104017	0 14 32 66 72 84 86 120 122 134 140 174 192 206	39623626428
SPT(14)	87667448123968681	0 48 70 90 118 126 160 168 202 210 238 258 280 328	42898491092
SPT(14)	87667466113308157	0 4 10 30 70 72 76 150 154 156 196 216 222 226	60887830568