Prime p₀= 404886951969657761 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 88 2 34 2 28 2 58 2 22 2 (?)
a_n: 0 2 90 92 126 128 156 158 216 218 240 242
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: 242
Found by: Cruncher Pete
db: batch=70, k=12, 88 34 28 58 22

SPT(14)	404886887505371599	0 12 40 60 142 160 168 172 180 198 280 300 328 340	-64464286162
SPT(14)	404886905609470129	0 28 42 48 70 72 94 108 130 132 154 160 174 202	-46360187632
SPT(14)	404886912925245169	0 34 42 90 100 112 172 282 342 354 364 412 420 454	-39044412592
SPT(14)	404886917509253357	0 72 92 110 120 122 162 182 222 224 234 252 272 344	-34460404404
SPT(14)	404886926109368609	0 18 54 90 110 132 162 200 230 252 272 308 344 362	-25860289152
SPT(14)	404886938213154701	0 6 12 20 90 120 132 176 188 218 288 296 302 308	-13756503060
TPT(12)	404886971139641909	0 2 18 20 42 44 72 74 78 80 90 92	19169984148
SPT(14)	404886982903352041	0 66 96 108 130 162 166 192 196 228 250 262 292 358	30933694280
SPT(14)	404886993689278439	0 8 30 54 78 120 128 180 188 230 254 278 300 308	41719620678
SPT(14)	404887026898778321	0 8 56 78 122 126 146 192 212 216 260 282 330 338	74929120560
TPT(12)	404887037250410567	0 2 54 56 210 212 240 242 264 266 282 284	85280752806