Prime p₀= 408617304396336221 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 10 2 70 2 46 2 118 2 (?)
a_n: 0 2 6 8 18 20 90 92 138 140 258 260
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, 4 10 70 46 118

SPT(14)	408617243305717001	0 12 78 90 98 128 180 248 300 330 338 350 416 428	-61090619220
SPT(14)	408617255030979433	0 40 60 66 70 106 108 148 150 186 190 196 216 256	-49365356788
TPT(12)	408617263541577941	0 2 270 272 336 338 426 428 516 518 576 578	-40854758280
SPT(14)	408617266539693863	0 38 78 80 156 158 198 248 288 290 366 368 408 446	-37856642358
SPT(14)	408617285164157309	0 8 32 44 50 74 84 158 168 192 198 210 234 242	-19232178912
SPT(14)	408617297314329529	0 12 54 72 82 90 100 324 334 342 352 370 412 424	-7082006692
SPT(14)	408617307092729381	0 8 30 66 86 96 98 150 152 162 182 218 240 248	2696393160
SPT(14)	408617311290726191	0 20 38 56 66 90 92 96 98 122 132 150 168 188	6894389970
SPT(14)	408617315948164459	0 34 78 82 100 118 142 180 204 222 240 244 288 322	11551828238
SPT(14)	408617323521988181	0 2 12 20 42 72 122 156 206 236 258 266 276 278	19125651960
SPT(14)	408617324359893067	0 16 24 46 60 84 94 102 112 136 150 172 180 196	19963556846