Prime p₀= 257919253355150741 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 88 2 28 2 40 2 28 2 (?)
a_n: 0 2 6 8 96 98 126 128 168 170 198 200
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: 200
Found by: DoctorNow
db: batch=69, k=12, 4 88 28 40 28

TPT(12)	257919124187849417	0 2 12 14 54 56 72 74 102 104 144 146	-129167301324
TPT(12)	257919133901305907	0 2 84 86 114 116 120 122 132 134 174 176	-119453844834
SPT(14)	257919176307866407	0 24 42 52 60 112 126 130 144 196 204 214 232 256	-77047284334
SPT(14)	257919229757751559	0 4 54 84 90 112 144 148 180 202 208 238 288 292	-23597399182
SPT(14)	257919233150330093	0 14 30 66 108 116 146 168 198 206 248 284 300 314	-20204820648
SPT(14)	257919251965946297	0 20 42 62 74 114 156 200 242 282 294 314 336 356	-1389204444
SPT(14)	257919265362007217	0 2 30 42 50 72 92 132 152 174 182 194 222 224	12006856476
SPT(14)	257919265819458361	0 10 40 42 88 108 118 150 160 180 226 228 258 268	12464307620
SPT(14)	257919289536866261	0 50 56 90 96 98 152 156 210 212 218 252 258 308	36181715520
SPT(14)	257919307297861213	0 4 70 88 90 96 114 130 148 154 156 174 240 244	53942710472
TPT(12)	257919314550091079	0 2 12 14 18 20 42 44 240 242 270 272	61194940338