Prime p₀= 144299103796895651 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 46 2 40 2 124 2 28 2 10 2 (?)
a_n: 0 2 48 50 90 92 216 218 246 248 258 260
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: 260
Found by: emoga
db: batch=67, k=12, 46 40 124 28 10

SPT(14)	144298897038887599	0 12 24 42 64 82 120 142 180 198 220 238 250 262	-206758008052
SPT(16)	144298991779960879	0 28 30 70 78 102 108 112 180 184 190 214 222 262 264 292	-112016934772
SPT(14)	144298998445617077	0 2 6 62 72 86 96 140 150 164 174 230 234 236	-105351278574
TPT(12)	144299040175994057	0 2 12 14 54 56 90 92 132 134 210 212	-63620901594
SPT(14)	144299040783463411	0 28 46 52 82 108 112 156 160 186 216 222 240 268	-63013432240
SPT(14)	144299069985354017	0 42 44 54 156 164 182 264 282 290 392 402 404 446	-33811541634
TPT(12)	144299106124456781	0 2 78 80 108 110 120 122 168 170 180 182	2327561130
SPT(14)	144299107984938917	0 6 14 62 84 114 140 156 182 212 234 282 290 296	4188043266
TPT(12)	144299131340986199	0 2 12 14 30 32 90 92 282 284 348 350	27544090548
SPT(14)	144299134762573369	0 18 22 28 42 64 82 90 108 130 144 150 154 172	30965677718
SPT(14)	144299137167397711	0 6 10 42 72 76 100 102 126 130 160 192 196 202	33370502060