Prime p₀= 2524092999151467377 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 10 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 72 74 102 104 132 134
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: 134
Found by: [AF>Linux]Rogue 9
db: batch=82, k=12, 2 28 2 28 2 10

SPT(16)	2524091917186299073	0 6 28 34 40 66 70 76 138 144 148 174 180 186 208 214	-1081965168304
STPT(12)	2524092420898649969	0 2 12 14 42 44 60 62 90 92 102 104	-578252817408
SPT(16)	2524092422106640373	0 8 18 30 84 114 146 174 200 228 260 290 344 356 366 374	-577044827004
TPT(14)	2524092494288123597	0 2 54 56 60 62 102 104 150 152 192 194 252 254	-504863343780
SPT(16)	2524092569802913097	0 14 42 44 114 120 126 134 192 200 206 212 282 284 312 326	-429348554280
SPT(16)	2524092685431647293	0 6 34 94 120 144 150 204 220 274 280 304 330 390 418 424	-313719820084
TPT(14)	2524093549671045347	0 2 30 32 72 74 84 86 114 116 132 134 162 164	550519577970
STPT(10)	2524093609114873319	0 2 18 20 30 32 42 44 60 62	609963405942
SPT(16)	2524093790849751937	0 4 10 12 42 60 90 102 154 166 196 214 244 246 252 256	791698284560
SPT(16)	2524094169929371939	0 12 28 30 34 42 82 100 102 120 160 168 172 174 190 202	1170777904562
SPT(16)	2524094236517310647	0 2 12 26 42 56 80 92 144 156 180 194 210 224 234 236	1237365843270