Prime p₀= 566656805693318579 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 10 2 136 2 70 2 34 2 (?)
a_n: 0 2 30 32 42 44 180 182 252 254 288 290
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: 290
Found by: Coleslaw
db: batch=71, k=12, 28 10 136 70 34

SPT(14)	566656729859161157	0 32 74 80 110 140 164 210 234 264 294 300 342 374	-75834157422
SPT(14)	566656742880033899	0 38 90 92 132 140 162 260 282 290 330 332 384 422	-62813284680
SPT(14)	566656767711580807	0 10 34 84 160 162 172 174 184 186 262 312 336 346	-37981737772
SPT(16)	566656769920060997	0 30 36 62 80 114 144 204 212 272 302 336 354 380 386 416	-35773257582
SPT(14)	566656776481601719	0 30 60 64 72 90 114 130 154 172 180 184 214 244	-29211716860
SPT(16)	566656791000531289	0 10 22 24 70 112 132 148 204 220 240 282 328 330 342 352	-14692787290
SPT(14)	566656814022272789	0 32 50 54 60 84 92 162 170 194 200 204 222 254	8328954210
SPT(14)	566656815550171261	0 10 12 40 42 48 82 138 172 178 180 208 210 220	9856852682
SPT(14)	566656815912235837	0 22 24 34 52 60 70 126 136 144 162 172 174 196	10218917258
TPT(12)	566656823149676009	0 2 78 80 102 104 258 260 282 284 312 314	17456357430
TPT(12)	566656843645942001	0 2 36 38 66 68 138 140 198 200 210 212	37952623422