Prime p₀= 78078145182306989 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 106 2 40 2 130 2 76 2 46 2 (?)
a_n: 0 2 108 110 150 152 282 284 360 362 408 410
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: 410
Found by: emoga
db: batch=67, k=12, 106 40 130 76 46

SPT(14)	78078068849013811	0 12 40 42 76 88 90 118 120 132 166 168 196 208	-76333293178
TPT(12)	78078098195539229	0 2 12 14 30 32 60 62 102 104 168 170	-46986767760
SPT(14)	78078112954467317	0 6 20 24 54 60 80 90 110 116 146 150 164 170	-32227839672
SPT(14)	78078113873200211	0 2 30 36 50 66 78 80 92 108 122 128 156 158	-31309106778
SPT(14)	78078136651063001	0 18 48 56 90 102 116 162 176 188 222 230 260 278	-8531243988
SPT(14)	78078143317516999	0 30 34 42 54 60 82 90 112 118 130 138 142 172	-1864789990
SPT(14)	78078145762839143	0 6 26 54 74 84 96 98 110 120 140 168 188 194	580532154
SPT(14)	78078149430937373	0 68 78 84 86 110 120 134 144 168 170 176 186 254	4248630384
SPT(14)	78078172644242689	0 34 78 88 118 120 150 172 202 204 234 244 288 322	27461935700
SPT(14)	78078181201196021	0 18 42 72 110 128 140 240 252 270 308 338 362 380	36018889032
SPT(14)	78078182571446357	0 14 20 42 72 86 110 186 210 224 254 276 282 296	37389139368