Prime p₀= 144278792112350741 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 154 2 40 2 106 2 52 2 58 2 (?)
a_n: 0 2 156 158 198 200 306 308 360 362 420 422
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: 422
Found by: Tomáš Brada
db: batch=67, k=12, 154 40 106 52 58

TPT(12)	144278731806218921	0 2 30 32 60 62 90 92 168 170 198 200	-60306131820
SPT(14)	144278732612339197	0 22 52 60 94 96 120 136 160 162 196 204 234 256	-59500011544
SPT(14)	144278747497774063	0 30 40 58 88 108 130 234 256 276 306 324 334 364	-44614576678
TPT(12)	144278752831236407	0 2 42 44 72 74 114 116 150 152 180 182	-39281114334
SPT(16)	144278772705576071	0 56 66 80 90 146 168 170 276 278 300 356 366 380 390 446	-19406774670
SPT(14)	144278782083922081	0 16 18 22 58 88 96 112 120 150 186 190 192 208	-10028428660
SPT(14)	144278798405603231	0 30 32 68 86 108 110 198 200 222 240 276 278 308	6293252490
SPT(18)	144278808607233577	0 12 46 70 82 112 120 142 156 340 354 376 384 414 426 450 484 496	16494882836
SPT(14)	144278812063995109	0 18 22 42 48 64 90 112 138 154 160 180 184 202	19951644368
SPT(14)	144278813796127181	0 12 42 72 86 92 150 182 240 246 260 290 320 332	21683776440
SPT(14)	144278827793240177	0 14 72 90 116 156 164 192 200 240 266 284 342 356	35680889436