Prime p₀= 146553983958232427 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 28 2 76 2 58 2 16 2 (?)
a_n: 0 2 24 26 54 56 132 134 192 194 210 212
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: 212
Found by: emoga
db: batch=67, k=12, 22 28 76 58 16

SPT(14)	146553968096538719	0 2 68 78 104 120 138 164 182 198 224 234 300 302	-15861693708
SPT(14)	146553970867644217	0 12 54 70 82 126 142 174 190 234 246 262 304 316	-13090588210
SPT(14)	146553973074488591	0 8 20 42 66 80 86 132 138 152 176 198 210 218	-10883743836
SPT(14)	146553979679885363	0 36 48 66 78 134 150 164 180 236 248 266 278 314	-4278347064
SPT(14)	146553982165964533	0 4 84 90 118 144 154 234 244 270 298 304 384 388	-1792267894
SPT(14)	146553983422757387	0 2 60 86 120 126 144 152 170 176 210 236 294 296	-535475040
SPT(14)	146554001138486521	0 52 66 90 112 126 130 132 136 150 172 196 210 262	17180254094
SPT(14)	146554030229177261	0 12 18 20 26 140 218 270 348 462 468 470 476 488	46270944834
SPT(16)	146554033724532023	0 6 14 24 66 78 104 108 266 270 296 308 350 360 368 374	49766299596
SPT(14)	146554041361409197	0 22 54 90 172 180 204 220 244 252 334 370 402 424	57403176770
TPT(12)	146554057032520517	0 2 42 44 90 92 120 122 144 146 210 212	73074288090