Prime p₀= 402557381020296947 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 82 2 136 2 58 2 16 2 22 2 (?)
a_n: 0 2 84 86 222 224 282 284 300 302 324 326
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: 326
Found by: Cruncher Pete
db: batch=70, k=12, 82 136 58 16 22

SPT(14)	402557285029206029	0 8 24 92 108 144 162 170 188 224 240 308 324 332	-95991090918
TPT(12)	402557318311972007	0 2 30 32 42 44 72 74 84 86 174 176	-62708324940
SPT(14)	402557321196624001	0 28 46 52 118 150 192 196 238 270 336 342 360 388	-59823672946
SPT(14)	402557338210040249	0 18 32 42 48 60 62 90 92 104 110 120 134 152	-42810256698
SPT(14)	402557338611358747	0 24 34 40 70 84 126 130 172 186 216 222 232 256	-42408938200
SPT(14)	402557338934209799	0 14 30 42 72 84 90 92 98 110 140 152 168 182	-42086087148
TPT(12)	402557382279302321	0 2 30 32 36 38 156 158 198 200 366 368	1259005374
SPT(14)	402557383776375193	0 4 18 34 48 58 66 178 186 196 210 226 240 244	2756078246
SPT(14)	402557391862991447	0 56 66 84 90 96 110 180 194 200 206 224 234 290	10842694500
SPT(14)	402557405188795459	0 10 30 42 58 72 84 88 100 114 130 142 162 172	24168498512
SPT(14)	402557460613793659	0 10 42 52 88 108 130 150 172 192 228 238 270 280	79593496712