Prime p₀= 382560777283512869 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 118 2 58 2 40 2 10 2 (?)
a_n: 0 2 18 20 138 140 198 200 240 242 252 254
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: 254
Found by: Cruncher Pete
db: batch=70, k=12, 16 118 58 40 10

SPT(14)	382560722377416481	0 42 70 120 126 132 166 246 280 286 292 342 370 412	-54906096388
SPT(14)	382560728087451421	0 28 30 48 58 78 106 132 160 180 190 208 210 238	-49196061448
STPT(10)	382560748808642309	0 2 12 14 90 92 168 170 180 182	-28474870560
SPT(14)	382560752887222951	0 18 40 52 72 90 132 136 178 196 216 228 250 268	-24396289918
STPT(10)	382560759492725249	0 2 42 44 60 62 78 80 120 122	-17790787620
SPT(14)	382560763509668921	0 2 36 50 62 78 146 192 260 276 288 302 336 338	-13773843948
SPT(14)	382560799680931933	0 28 48 124 144 178 234 274 330 364 384 460 480 508	22397419064
SPT(14)	382560816410507491	0 12 40 42 58 60 72 196 208 210 226 228 256 268	39126994622
TPT(12)	382560823547520509	0 2 12 14 78 80 132 134 168 170 192 194	46264007640
SPT(14)	382560850818284011	0 30 48 52 66 82 90 178 186 202 216 220 238 268	73534771142
SPT(14)	382560865841710103	0 6 14 56 66 78 104 120 146 158 168 210 218 224	88558197234