Prime p₀= 2562109653188216777 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 22 2 4 2 22 2 58 2 (?)
a_n: 0 2 60 62 84 86 90 92 114 116 174 176
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: 176
Found by: Penguin
db: batch=82, k=12, 2 58 2 22 2 4

TPT(14)	2562107540270807717	0 2 12 14 24 26 42 44 114 116 222 224 234 236	-2112917409060
SPT(16)	2562107561212271749	0 18 40 42 112 132 138 154 228 244 250 270 340 342 364 382	-2091975945028
SPT(16)	2562108277269559009	0 4 18 90 94 118 150 160 222 232 264 288 292 364 378 382	-1375918657768
STPT(10)	2562108864726607319	0 2 12 14 30 32 48 50 60 62	-788461609458
SPT(16)	2562109223202045701	0 38 48 78 86 90 92 98 150 156 158 162 170 200 210 248	-429986171076
SPT(16)	2562109531643749151	0 8 30 38 42 78 122 138 182 198 242 278 282 290 312 320	-121544467626
SPT(16)	2562110166295754653	0 24 90 106 138 168 204 216 238 250 286 316 348 364 430 454	513107537876
SPT(16)	2562110349564458321	0 30 68 72 80 110 126 128 210 212 228 258 266 270 308 338	696376241544
STPT(10)	2562110956780341467	0 2 54 56 72 74 90 92 144 146	1303592124690
SPT(16)	2562111276625950611	0 42 72 86 90 212 216 240 308 332 336 458 462 476 506 548	1623437733834
SPT(16)	2562111303185794219	0 10 60 82 142 150 198 228 304 334 382 390 450 472 522 532	1649997577442