Prime p₀= 1267911290202763901 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 4 2 40 2 28 2 40 2 4 2 (?)
a_n: 0 2 6 8 48 50 78 80 120 122 126 128
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: 128
Found by: Megacruncher
db: batch=77, k=12, 2 4 2 40 2 28

STPT(10)	1267909687174159439	0 2 12 14 90 92 168 170 180 182	-1603028604462
SPT(16)	1267909848792918139	0 4 40 70 132 160 172 184 198 210 222 250 312 342 378 382	-1441409845762
TPT(16)	1267910384622449669	0 2 12 14 162 164 168 170 192 194 330 332 462 464 498 500	-905580314232
SPT(16)	1267910518892700971	0 30 32 38 60 98 110 120 200 210 222 260 282 288 290 320	-771310062930
SPT(16)	1267910544228475111	0 18 30 60 82 90 112 118 180 186 208 216 238 268 280 298	-745974288790
SPT(18)	1267911286370162801	0 38 50 68 120 122 152 170 206 222 258 276 306 308 360 378 390 428	-3832601100
SPT(16)	1267911582046888433	0 14 20 26 30 56 68 78 146 156 168 194 198 204 210 224	291844124532
SPT(16)	1267911614719163333	0 24 36 56 90 110 134 138 206 210 234 254 288 308 320 344	324516399432
TPT(14)	1267911711524208629	0 2 132 134 168 170 222 224 270 272 300 302 348 350	421321444728
SPT(18)	1267911906448381267	0 16 42 52 54 82 94 120 156 160 196 222 234 262 264 274 300 316	616245617366
STPT(10)	1267912197128624189	0 2 18 20 30 32 42 44 60 62	906925860288