Prime p₀= 400278308223298277 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 10 2 58 2 34 2 310 2 (?)
a_n: 0 2 12 14 24 26 84 86 120 122 432 434
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: 434
Found by: Ralfy
db: batch=70, k=12, 10 10 58 34 310

SPT(14)	400278283996622401	0 10 16 30 42 52 100 108 156 166 178 192 198 208	-24226675876
SPT(14)	400278284855309611	0 48 70 76 90 108 126 160 178 196 210 216 238 286	-23367988666
TPT(12)	400278299237064509	0 2 30 32 42 44 132 134 162 164 198 200	-8986233768
SPT(14)	400278303712305371	0 2 26 30 48 72 80 138 146 170 188 192 216 218	-4510992906
SPT(14)	400278307126023847	0 36 42 72 124 132 154 162 184 192 244 274 280 316	-1097274430
SPT(14)	400278307912815361	0 16 40 42 60 100 108 130 138 178 196 198 222 238	-310482916
SPT(14)	400278317410776029	0 32 68 102 120 144 170 192 218 242 260 294 330 362	9187477752
TPT(12)	400278332530759379	0 2 12 14 30 32 168 170 210 212 240 242	24307461102
TPT(12)	400278345292503779	0 2 78 80 90 92 132 134 162 164 192 194	37069205502
TPT(12)	400278351550592027	0 2 30 32 102 104 132 134 144 146 162 164	43327293750
SPT(14)	400278354047147273	0 20 68 74 96 144 168 206 230 278 300 306 354 374	45823848996