Prime p₀= 740708887582582097 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 22 2 4 2 22 2 58 2 (?)
a_n: 0 2 60 62 84 86 90 92 114 116 174 176
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: 176
Found by: Theadalus
db: batch=73, k=12, 2 58 2 22 2 4

SPT(16)	740707997022179519	0 14 102 114 132 144 182 204 320 342 380 392 410 422 510 524	-890560402578
TPT(14)	740708173253404619	0 2 42 44 72 74 90 92 198 200 258 260 300 302	-714329177478
STPT(10)	740708411894477207	0 2 30 32 42 44 54 56 84 86	-475688104890
SPT(16)	740708536859877827	0 14 24 50 72 90 120 140 156 176 206 224 246 272 282 296	-350722704270
SPT(16)	740708644957428881	0 26 32 48 56 62 66 68 180 182 186 192 200 216 222 248	-242625153216
SPT(16)	740708710120895233	0 16 120 144 148 156 174 190 264 280 298 306 310 334 438 454	-177461686864
SPT(16)	740709025629790619	0 12 24 68 98 108 128 132 230 234 254 264 294 338 350 362	138047208522
TPT(14)	740709061388174771	0 2 48 50 60 62 96 98 138 140 180 182 198 200	173805592674
SPT(16)	740709303202921747	0 10 36 66 84 106 120 154 186 220 234 256 274 304 330 340	415620339650
STPT(10)	740709902847676427	0 2 30 32 42 44 54 56 84 86	1015265094330
SPT(16)	740710018026996733	0 36 60 130 196 238 240 256 270 286 288 330 396 466 490 526	1130444414636