Prime p₀= 408432780767004611 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 46 2 10 2 28 2 34 2 70 2 (?)
a_n: 0 2 48 50 60 62 90 92 126 128 198 200
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: Cruncher Pete
db: batch=70, k=12, 46 10 28 34 70

SPT(14)	408432707433299287	0 22 60 72 82 84 102 124 142 144 154 166 204 226	-73333705324
TPT(12)	408432708080224757	0 2 24 26 72 74 114 116 180 182 210 212	-72686779854
SPT(14)	408432708958520663	0 60 84 104 186 198 230 264 296 308 390 410 434 494	-71808483948
TPT(14)	408432723827154149	0 2 90 92 132 134 168 170 180 182 210 212 222 224	-56939850462
SPT(14)	408432754891437907	0 12 24 42 52 54 70 96 112 114 124 142 154 166	-25875566704
SPT(16)	408432763463038339	0 12 18 54 78 100 198 202 210 214 312 334 358 394 400 412	-17303966272
SPT(16)	408432819428012719	0 42 70 72 88 112 162 172 228 238 288 312 328 330 358 400	38661008108
SPT(14)	408432823280455613	0 14 24 38 78 84 90 248 254 260 300 314 324 338	42513451002
SPT(14)	408432837180895399	0 34 90 118 148 162 178 234 250 264 294 322 378 412	56413890788
SPT(14)	408432841434333713	0 26 84 90 104 116 144 176 204 216 230 236 294 320	60667329102
STPT(10)	408432841601807147	0 2 30 32 72 74 114 116 144 146	60834802536