Prime p₀= 78078098195539229 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 16 2 28 2 40 2 64 2 (?)
a_n: 0 2 12 14 30 32 60 62 102 104 168 170
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: 170
Found by: emoga
db: batch=67, k=12, 10 16 28 40 64

SPT(14)	78077994701625859	0 12 22 28 48 54 114 118 178 184 204 210 220 232	-103493913370
SPT(16)	78077996023466437	0 6 52 60 84 94 102 120 136 154 162 172 196 204 250 256	-102172072792
TPT(12)	78077998983735731	0 2 30 32 78 80 120 122 138 140 180 182	-99211803498
TPT(12)	78078016352789261	0 2 48 50 90 92 96 98 180 182 306 308	-81842749968
SPT(14)	78078024102270193	0 16 28 58 84 130 156 238 264 310 336 366 378 394	-74093269036
SPT(14)	78078068849013811	0 12 40 42 76 88 90 118 120 132 166 168 196 208	-29346525418
SPT(14)	78078112954467317	0 6 20 24 54 60 80 90 110 116 146 150 164 170	14758928088
SPT(14)	78078113873200211	0 2 30 36 50 66 78 80 92 108 122 128 156 158	15677660982
SPT(14)	78078136651063001	0 18 48 56 90 102 116 162 176 188 222 230 260 278	38455523772
SPT(14)	78078143317516999	0 30 34 42 54 60 82 90 112 118 130 138 142 172	45121977770
TPT(12)	78078145182306989	0 2 108 110 150 152 282 284 360 362 408 410	46986767760