Prime p₀= 378625843137212519 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 70 2 64 2 118 2 52 2 (?)
a_n: 0 2 30 32 102 104 168 170 288 290 342 344
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: 344
Found by: Cruncher Pete
db: batch=70, k=12, 28 70 64 118 52

SPT(14)	378625780626185203	0 4 46 96 118 124 156 268 300 306 328 378 420 424	-62511027316
SPT(14)	378625820778394291	0 16 42 72 82 90 100 102 112 120 130 160 186 202	-22358818228
SPT(14)	378625837121788661	0 18 56 62 66 98 152 186 240 272 276 282 320 338	-6015423858
SPT(14)	378625838504949601	0 10 60 70 82 100 126 142 168 186 198 208 258 268	-4632262918
SPT(14)	378625838906592947	0 66 104 132 134 140 150 206 216 222 224 252 290 356	-4230619572
TPT(12)	378625839870252197	0 2 12 14 42 44 60 62 150 152 210 212	-3266960322
SPT(14)	378625847346185479	0 28 42 52 88 102 118 162 178 192 228 238 252 280	4208972960
SPT(16)	378625853582143229	0 14 18 20 54 90 110 144 194 228 248 284 318 320 324 338	10444930710
TPT(12)	378625857632216417	0 2 42 44 54 56 60 62 150 152 222 224	14495003898
SPT(14)	378625888771691221	0 22 42 48 58 72 90 148 166 180 190 196 216 238	45634478702
TPT(12)	378625889304852599	0 2 42 44 132 134 180 182 222 224 300 302	46167640080