Prime p₀= 28467644788690031 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 136 2 10 2 58 2 76 2 16 2 (?)
a_n: 0 2 138 140 150 152 210 212 288 290 306 308
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: 308
Found by: amazing
db: batch=65, k=12, 136 10 58 76 16

SPT(14)	28467629735905361	0 30 56 66 92 150 176 192 218 276 302 312 338 368	-15052784670
STPT(10)	28467634819730789	0 2 42 44 90 92 138 140 180 182	-9968959242
SPT(14)	28467635426624861	0 20 42 98 102 132 150 158 176 206 210 266 288 308	-9362065170
SPT(16)	28467640611095963	0 14 68 98 104 120 128 146 168 186 194 210 216 246 300 314	-4177594068
SPT(14)	28467641084554951	0 10 16 28 30 42 52 66 76 88 90 102 108 118	-3704135080
SPT(14)	28467644511761599	0 4 22 60 70 72 82 102 112 114 124 162 180 184	-276928432
SPT(16)	28467661790262907	0 4 16 46 70 90 144 174 196 226 280 300 324 354 366 370	17001572876
SPT(14)	28467668152957343	0 78 120 144 164 200 360 368 528 564 584 608 650 728	23364267312
SPT(14)	28467686747694461	0 2 36 56 68 72 122 126 176 180 192 212 246 248	41959004430
SPT(14)	28467705612986203	0 6 16 36 54 84 120 160 196 226 244 264 274 280	60824296172
TPT(12)	28467705762965837	0 2 12 14 54 56 60 62 90 92 174 176	60974275806