Prime p₀= 2568533827241423147 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 16 2 22 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 54 56 72 74 84 86
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: 86
Found by: [SG-FC] hl
db: batch=82, k=12, 2 10 2 16 2 22

SPT(16)	2568533084054432749	0 18 30 34 52 88 102 112 150 160 174 210 228 232 244 262	-743186990398
SPT(16)	2568533316488095469	0 2 30 32 42 50 108 120 122 134 192 200 210 212 240 242	-510753327678
SPT(16)	2568533581426718407	0 22 36 60 64 66 102 106 150 154 190 192 196 220 234 256	-245814704740
SPT(16)	2568533686467017999	0 14 20 30 78 90 104 114 134 144 158 170 218 228 234 248	-140774405148
STPT(10)	2568533716242446387	0 2 30 32 42 44 54 56 84 86	-110998976760
STPT(10)	2568533772415576289	0 2 42 44 60 62 78 80 120 122	-54825846858
TPT(14)	2568534287868140399	0 2 192 194 300 302 372 374 420 422 432 434 558 560	460626717252
STPT(10)	2568534543358157189	0 2 12 14 30 32 48 50 60 62	716116734042
TPT(14)	2568534545226597719	0 2 30 32 78 80 90 92 210 212 228 230 300 302	717985174572
SPT(16)	2568534699654132551	0 6 80 90 146 156 198 222 266 290 332 342 398 408 482 488	872412709404
STPT(10)	2568534777844597139	0 2 42 44 90 92 138 140 180 182	950603173992