Prime p₀= 916678736484959939 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 58 2 4 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 78 80 138 140 150 152
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: 152
Found by: Theadalus
db: batch=76, k=12, 2 10 2 58 2 4

SPT(16)	916677271656312487	0 46 66 132 150 154 210 216 220 226 282 286 304 370 390 436	-1464828647452
STPT(10)	916677480817095587	0 2 42 44 72 74 102 104 144 146	-1255667864352
SPT(16)	916678219475466257	0 56 62 110 122 132 216 272 390 446 530 540 552 600 606 662	-517009493682
SPT(16)	916678250694154057	0 4 30 36 40 64 72 130 156 214 222 246 250 256 282 286	-485790805882
STPT(10)	916678355994116171	0 2 30 32 78 80 126 128 156 158	-380490843768
SPT(16)	916678356252595753	0 6 10 60 90 144 160 168 196 204 220 274 304 354 358 364	-380232364186
SPT(16)	916678893717794839	0 52 90 118 130 132 172 192 220 240 280 282 294 322 360 412	157232834900
STPT(10)	916679102533587719	0 2 18 20 30 32 42 44 60 62	366048627780
SPT(16)	916679106751989149	0 8 44 62 74 90 134 162 350 378 422 438 450 468 504 512	370267029210
SPT(16)	916679305917496883	0 48 54 60 84 98 110 138 236 264 276 290 314 320 326 374	569432536944
TPT(14)	916679461117750871	0 2 36 38 78 80 156 158 168 170 186 188 258 260	724632790932