Prime p₀= 2510262662324135657 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: JonS
db: batch=82, k=12, 2 10 2 10 2 4

STPT(10)	2510262029395598519	0 2 18 20 30 32 42 44 60 62	-632928537138
SPT(16)	2510262127360780739	0 24 50 92 114 162 174 182 282 290 302 350 372 414 440 464	-534963354918
SPT(16)	2510262188873745263	0 18 26 68 86 116 138 146 180 188 210 240 258 300 308 326	-473450390394
SPT(16)	2510262189592975619	0 18 32 68 72 114 120 194 228 302 308 350 354 390 404 422	-472731160038
SPT(16)	2510262275671055651	0 26 62 78 146 152 182 186 302 306 336 342 410 426 462 488	-386653080006
STPT(10)	2510262611282261117	0 2 60 62 102 104 144 146 204 206	-51041874540
SPT(16)	2510262752082951557	0 20 24 54 86 96 146 164 216 234 284 294 326 356 360 380	89758815900
SPT(16)	2510262774563351659	0 10 34 60 64 108 130 148 150 168 190 234 238 264 288 298	112239216002
TPT(14)	2510262826053831029	0 2 30 32 192 194 228 230 240 242 420 422 432 434	163729695372
SPT(16)	2510263300825939429	0 30 42 64 82 114 138 168 184 214 238 270 288 310 322 352	638501803772
STPT(10)	2510263468077064727	0 2 24 26 42 44 60 62 84 86	805752929070