Prime p₀= 5817351306696779 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 64 2 22 2 16 2 16 2 (?)
a_n: 0 2 42 44 108 110 132 134 150 152 168 170
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: 170
Found by: Egon olsen
db: batch=62, k=12, 40 64 22 16 16

SPT(16)	5817321673772101	0 28 30 36 52 76 126 132 136 142 192 216 232 238 240 268	-29632924678
SPT(14)	5817328619180257	0 12 46 54 90 130 132 154 156 196 232 240 274 286	-22687516522
SPT(14)	5817331687073659	0 64 100 130 174 180 202 210 232 238 282 312 348 412	-19619623120
SPT(14)	5817341446184753	0 30 38 66 80 114 156 158 200 234 248 276 284 314	-9860512026
SPT(14)	5817345470834071	0 6 40 58 126 130 132 166 168 172 240 258 292 298	-5835862708
SPT(14)	5817349706852737	0 6 36 40 84 144 180 190 226 286 330 334 364 370	-1599844042
SPT(14)	5817355078515341	0 36 126 140 152 162 228 260 326 336 348 362 452 488	3771818562
TPT(12)	5817359503932089	0 2 120 122 180 182 192 194 222 224 240 242	8197235310
SPT(14)	5817363852214093	0 4 40 46 64 160 186 358 384 480 498 504 540 544	12545517314
SPT(14)	5817395145045761	0 6 56 102 140 146 158 210 222 228 266 312 362 368	43838348982
TPT(12)	5817397618283591	0 2 18 20 90 92 156 158 198 200 228 230	46311586812