Prime p₀= 2260070413842957851 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 76 2 88 2 28 2 88 2 76 2 (?)
a_n: 0 2 78 80 168 170 198 200 288 290 366 368
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: 368
Found by: Orange Kid
db: batch=81, k=12, 2 76 2 88 2 28

SPT(16)	2260069044986381543	0 48 56 66 68 90 98 158 168 228 236 258 260 270 278 326	-1368856576308
STPT(10)	2260069090073627057	0 2 30 32 42 44 54 56 84 86	-1323769330794
SPT(16)	2260069235636027201	0 8 26 36 38 60 66 96 122 152 158 180 182 192 210 218	-1178206930650
SPT(16)	2260069398095253523	0 4 70 120 148 168 246 256 258 268 346 366 394 444 510 514	-1015747704328
STPT(10)	2260069430923416989	0 2 30 32 60 62 90 92 120 122	-982919540862
STPT(10)	2260069514744042717	0 2 42 44 72 74 102 104 144 146	-899098915134
SPT(16)	2260070499131937227	0 2 42 50 72 134 170 180 194 204 240 302 324 332 372 374	85288979376
SPT(16)	2260070581523582297	0 2 12 126 140 144 150 182 264 296 302 306 320 434 444 446	167680624446
SPT(16)	2260070882374650173	0 14 44 56 66 96 140 170 174 204 248 278 288 300 330 344	468531692322
SPT(16)	2260070956784284949	0 32 42 92 114 140 152 162 260 270 282 308 330 380 390 422	542941327098
TPT(14)	2260071081665847641	0 2 6 8 36 38 48 50 78 80 120 122 156 158	667822889790