Prime p₀= 586966645085042219 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 70 2 16 2 148 2 16 2 10 2 (?)
a_n: 0 2 72 74 90 92 240 242 258 260 270 272
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: 272
Found by: scrap
db: batch=71, k=12, 70 16 148 16 10

SPT(14)	586966608985680397	0 36 60 64 94 96 102 154 160 162 192 196 220 256	-36099361822
SPT(14)	586966616425303591	0 10 52 78 130 136 142 156 162 168 220 246 288 298	-28659738628
TPT(12)	586966629724041029	0 2 138 140 210 212 222 224 282 284 288 290	-15361001190
SPT(14)	586966630978655309	0 42 54 72 78 90 128 144 182 194 200 218 230 272	-14106386910
SPT(14)	586966631784204953	0 8 14 30 50 98 110 138 150 198 218 234 240 248	-13300837266
TPT(12)	586966634040219149	0 2 12 14 78 80 138 140 162 164 210 212	-11044823070
SPT(14)	586966649511213131	0 2 12 56 68 80 128 150 198 210 222 266 276 278	4426170912
SPT(14)	586966654501374047	0 42 50 60 66 102 104 162 164 200 206 216 224 266	9416331828
SPT(14)	586966658112814121	0 48 60 80 102 128 168 230 270 296 318 338 350 398	13027771902
SPT(14)	586966658146455151	0 28 52 76 90 118 130 168 180 208 222 246 270 298	13061412932
SPT(14)	586966695281192927	0 30 60 110 116 126 162 200 236 246 252 302 332 362	50196150708