Prime p₀= 408431699733399701 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 22 2 148 2 16 2 28 2 (?)
a_n: 0 2 36 38 60 62 210 212 228 230 258 260
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: 260
Found by: Cruncher Pete
db: batch=70, k=12, 34 22 148 16 28

SPT(14)	408431484494990249	0 24 30 54 68 90 128 234 272 294 308 332 338 362	-215238409452
SPT(14)	408431528239591789	0 22 34 60 100 102 114 148 160 162 202 228 240 262	-171493807912
SPT(14)	408431528496193613	0 38 54 78 80 138 140 144 146 204 206 230 246 284	-171237206088
SPT(14)	408431571156772013	0 6 120 134 138 174 186 218 230 266 270 284 398 404	-128576627688
SPT(14)	408431589448733759	0 20 30 42 72 74 108 164 198 200 230 242 252 272	-110284665942
SPT(14)	408431644885612897	0 6 52 90 112 136 142 174 180 204 226 264 310 316	-54847786804
TPT(12)	408431735572311707	0 2 12 14 60 62 102 104 114 116 144 146	35838912006
SPT(14)	408431750470855387	0 6 22 34 94 112 132 184 204 222 282 294 310 316	50737455686
TPT(12)	408431778855292859	0 2 30 32 42 44 60 62 78 80 168 170	79121893158
SPT(14)	408431802444352891	0 66 100 112 142 168 172 336 340 366 396 408 442 508	102710953190
SPT(14)	408431810439187729	0 28 52 88 90 130 132 190 192 232 234 270 294 322	110705788028