Prime p₀= 404874558703533227 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 112 2 34 2 28 2 10 2 220 2 (?)
a_n: 0 2 114 116 150 152 180 182 192 194 414 416
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: 416
Found by: Cruncher Pete
db: batch=70, k=12, 112 34 28 10 220

SPT(14)	404874488383700281	0 22 36 42 70 78 88 150 160 168 196 202 216 238	-70319832946
TPT(12)	404874491243941217	0 2 30 32 72 74 90 92 114 116 174 176	-67459592010
SPT(14)	404874507593347643	0 8 74 90 98 134 144 164 174 210 218 234 300 308	-51110185584
SPT(14)	404874510163531613	0 6 44 56 66 74 126 188 240 248 258 270 308 314	-48540001614
SPT(14)	404874530515246037	0 12 24 32 56 60 80 156 176 180 204 212 224 236	-28188287190
TPT(12)	404874552468928769	0 2 12 14 78 80 162 164 168 170 210 212	-6234604458
SPT(14)	404874569164174843	0 10 24 66 96 118 138 196 216 238 268 310 324 334	10460641616
SPT(14)	404874622155751597	0 82 94 142 150 226 234 292 300 376 384 432 444 526	63452218370
SPT(14)	404874643028964149	0 2 12 18 42 48 90 110 152 158 182 188 198 200	84325430922
SPT(14)	404874653886032357	0 56 60 86 140 186 206 276 296 342 396 422 426 482	95182499130
SPT(14)	404874672044754287	0 12 26 32 60 80 120 122 162 182 210 216 230 242	113341221060