Prime p₀= 342424792526645837 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 82 2 34 2 88 2 22 2 (?)
a_n: 0 2 30 32 114 116 150 152 240 242 264 266
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: 266
Found by: Cruncher Pete
db: batch=70, k=12, 28 82 34 88 22

SPT(14)	342424701256482011	0 48 56 72 98 170 182 186 198 270 296 312 320 368	-91270163826
TPT(12)	342424724304856577	0 2 42 44 60 62 114 116 180 182 234 236	-68221789260
SPT(14)	342424727034671117	0 2 12 14 36 42 50 96 104 110 132 134 144 146	-65491974720
SPT(14)	342424731644475091	0 30 40 72 150 160 162 196 198 208 286 318 328 358	-60882170746
SPT(14)	342424774127018459	0 30 38 42 48 90 108 122 140 182 188 192 200 230	-18399627378
SPT(14)	342424781570297597	0 6 20 42 86 146 162 224 240 300 344 366 380 386	-10956348240
SPT(14)	342424830138069169	0 10 28 54 72 88 124 168 204 220 238 264 282 292	37611423332
SPT(14)	342424832731600573	0 6 10 34 36 40 64 210 234 238 240 264 268 274	40204954736
SPT(14)	342424839624823117	0 4 12 16 40 70 82 144 156 186 210 214 222 226	47098177280
SPT(18)	342424847669970881	0 56 72 78 92 102 116 156 158 180 182 222 236 246 260 266 282 338	55143325044
SPT(14)	342424848780325483	0 18 100 126 196 198 210 226 238 240 310 336 418 436	56253679646