Prime p₀= 1025585870280710987 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 22 2 28 2 64 2 28 2 22 2 (?)
a_n: 0 2 24 26 54 56 120 122 150 152 174 176
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: HenkM
db: batch=76, k=12, 2 22 2 28 2 64

TPT(14)	1025584062339973649	0 2 102 104 132 134 240 242 282 284 342 344 480 482	-1807940737338
STPT(10)	1025584287907409141	0 2 6 8 18 20 30 32 36 38	-1582373301846
SPT(16)	1025584629797587877	0 66 86 114 140 156 206 216 290 300 350 366 392 420 440 506	-1240483123110
SPT(16)	1025585564389093313	0 68 86 114 128 158 204 224 240 260 306 336 350 378 396 464	-305891617674
STPT(10)	1025585575881198881	0 2 6 8 48 50 90 92 96 98	-294399512106
SPT(16)	1025585771977950199	0 34 42 58 78 100 150 162 190 202 252 274 294 310 318 352	-98302760788
STPT(10)	1025586199828491617	0 2 30 32 42 44 54 56 84 86	329547780630
SPT(16)	1025586327652211107	0 4 16 40 70 72 90 94 132 136 154 156 186 210 222 226	457371500120
TPT(14)	1025586840378975827	0 2 12 14 42 44 192 194 210 212 252 254 264 266	970098264840
STPT(10)	1025587098571743809	0 2 12 14 90 92 168 170 180 182	1228291032822
SPT(16)	1025587215254930161	0 42 52 58 70 126 136 148 150 162 172 228 240 246 256 298	1344974219174