Prime p₀= 144299106124456781 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 28 2 10 2 46 2 10 2 (?)
a_n: 0 2 78 80 108 110 120 122 168 170 180 182
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: 182
Found by: emoga
db: batch=67, k=12, 76 28 10 46 10

SPT(16)	144298991779960879	0 28 30 70 78 102 108 112 180 184 190 214 222 262 264 292	-114344495902
SPT(14)	144298998445617077	0 2 6 62 72 86 96 140 150 164 174 230 234 236	-107678839704
TPT(12)	144299040175994057	0 2 12 14 54 56 90 92 132 134 210 212	-65948462724
SPT(14)	144299040783463411	0 28 46 52 82 108 112 156 160 186 216 222 240 268	-65340993370
SPT(14)	144299069985354017	0 42 44 54 156 164 182 264 282 290 392 402 404 446	-36139102764
TPT(12)	144299103796895651	0 2 48 50 90 92 216 218 246 248 258 260	-2327561130
SPT(14)	144299107984938917	0 6 14 62 84 114 140 156 182 212 234 282 290 296	1860482136
TPT(12)	144299131340986199	0 2 12 14 30 32 90 92 282 284 348 350	25216529418
SPT(14)	144299134762573369	0 18 22 28 42 64 82 90 108 130 144 150 154 172	28638116588
SPT(14)	144299137167397711	0 6 10 42 72 76 100 102 126 130 160 192 196 202	31042940930
STPT(10)	144299172397417727	0 2 30 32 42 44 54 56 84 86	66272960946