Prime p₀= 346240560283130087 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 10 2 16 2 40 2 34 2 (?)
a_n: 0 2 12 14 24 26 42 44 84 86 120 122
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: 122
Found by: Cruncher Pete
db: batch=70, k=12, 10 10 16 40 34

SPT(14)	346240497496895077	0 46 52 112 136 180 196 240 256 300 324 384 390 436	-62786235010
SPT(14)	346240507457196991	0 46 60 88 100 126 148 168 190 216 228 256 270 316	-52825933096
SPT(14)	346240515006524431	0 16 42 52 82 90 100 108 118 126 156 166 192 208	-45276605656
SPT(14)	346240518198674251	0 42 48 130 132 136 148 150 162 166 168 250 256 298	-42084455836
TPT(12)	346240520883369821	0 2 18 20 36 38 78 80 90 92 228 230	-39399760266
SPT(14)	346240531689146849	0 14 60 72 74 150 230 234 314 390 392 404 450 464	-28593983238
TPT(12)	346240564113908801	0 2 36 38 78 80 96 98 108 110 138 140	3830778714
SPT(14)	346240618963942193	0 8 30 74 86 126 170 234 278 318 330 374 396 404	58680812106
TPT(12)	346240621958154941	0 2 66 68 78 80 90 92 180 182 246 248	61675024854
SPT(14)	346240645811962469	0 12 14 44 54 80 84 98 102 128 138 168 170 182	85528832382
SPT(14)	346240649292610763	0 74 80 96 104 116 140 150 174 186 194 210 216 290	89009480676