Prime p₀= 1302358293726743129 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 10 2 4 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 48 50 60 62 90 92
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: 92
Found by: HenkM
db: batch=77, k=12, 2 28 2 10 2 4

SPT(16)	1302356621898999713	0 8 68 74 114 120 146 198 326 378 404 410 450 456 516 524	-1671827743416
TPT(14)	1302356829656199209	0 2 12 14 60 62 90 92 102 104 138 140 198 200	-1464070543920
SPT(16)	1302357100393132999	0 28 34 54 94 120 130 144 154 168 178 204 244 264 270 298	-1193333610130
SPT(16)	1302357272401826093	0 6 14 90 96 126 234 246 248 260 368 398 404 480 488 494	-1021324917036
SPT(16)	1302357327297345019	0 70 94 100 138 154 198 204 214 220 264 280 318 324 348 418	-966429398110
SPT(16)	1302358020977274913	0 10 18 28 36 54 84 136 138 190 220 238 246 256 264 274	-272749468216
SPT(16)	1302359032369526543	0 24 68 104 146 168 188 210 254 276 296 318 360 396 440 464	738642783414
STPT(10)	1302359208614451509	0 2 18 20 30 32 42 44 60 62	914887708380
SPT(16)	1302359546192445679	0 22 28 72 142 144 148 168 184 204 208 210 280 324 330 352	1252465702550
SPT(16)	1302359633877153871	0 10 42 70 96 108 112 162 166 216 220 232 258 286 318 328	1340150410742
SPT(16)	1302359680688947999	0 28 40 42 54 100 132 172 210 250 282 328 340 342 354 382	1386962204870