Prime p₀= 3000039252594400139 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 40 2 64 2 40 2 58 2 (?)
a_n: 0 2 60 62 102 104 168 170 210 212 270 272
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: eclipse99
db: batch=82, k=12, 2 58 2 40 2 64

STPT(10)	3000038029038735437	0 2 30 32 42 44 54 56 84 86	-1223555664702
SPT(16)	3000038356642424983	0 4 58 84 90 190 238 250 288 300 348 448 454 480 534 538	-895951975156
SPT(16)	3000038436816736379	0 60 72 80 102 110 120 150 212 242 252 260 282 290 302 362	-815777663760
SPT(16)	3000038877541202309	0 2 50 54 108 120 150 164 168 182 212 224 278 282 330 332	-375053197830
SPT(18)	3000039004861353557	0 20 26 36 50 90 104 126 174 182 230 252 266 306 320 330 336 356	-247733046582
SPT(16)	3000039083587073371	0 16 30 46 88 90 100 106 252 258 268 270 312 328 342 358	-169007326768
STPT(10)	3000039605312058479	0 2 18 20 30 32 42 44 60 62	352717658340
SPT(16)	3000039631581719059	0 4 34 42 54 84 90 102 112 124 130 160 172 180 210 214	378987318920
SPT(16)	3000039935791976461	0 10 18 30 60 70 112 130 138 156 198 208 238 250 258 268	683197576322
TPT(14)	3000040019782206197	0 2 24 26 30 32 42 44 144 146 234 236 240 242	767187806058
SPT(16)	3000040240292233301	0 20 66 92 168 210 228 242 276 290 308 350 426 452 498 518	987697833162