Prime p₀= 2501754002511095489 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 76 2 10 2 76 2 40 2 (?)
a_n: 0 2 42 44 120 122 132 134 210 212 252 254
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: 254
Found by: Ben
db: batch=82, k=12, 2 40 2 76 2 10

SPT(16)	2501752118579519191	0 16 42 52 66 70 72 136 156 220 222 226 240 250 276 292	-1883931576298
STPT(10)	2501752151783813471	0 2 6 8 48 50 90 92 96 98	-1850727282018
STPT(10)	2501752733134422587	0 2 30 32 42 44 54 56 84 86	-1269376672902
STPT(10)	2501752831648884587	0 2 54 56 72 74 90 92 144 146	-1170862210902
STPT(10)	2501753802624117401	0 2 6 8 48 50 90 92 96 98	-199886978088
STPT(10)	2501753886346791677	0 2 30 32 42 44 54 56 84 86	-116164303812
SPT(16)	2501754228750989297	0 12 44 56 134 176 182 192 254 264 270 312 390 402 434 446	226239893808
SPT(16)	2501754365457776713	0 18 34 36 48 70 96 138 196 238 264 286 298 300 316 334	362946681224
TPT(14)	2501754597713038079	0 2 60 62 192 194 252 254 282 284 360 362 408 410	595201942590
SPT(16)	2501754741473189347	0 22 82 112 120 166 172 186 190 204 210 256 264 294 354 376	738962093858
STPT(10)	2501755488278596601	0 2 6 8 18 20 30 32 36 38	1485767501112