Prime p₀= 2309069967834397487 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: Groo
db: batch=81, k=12, 2 10 2 10 2 4

STPT(10)	2309069026917150917	0 2 42 44 72 74 102 104 144 146	-940917246570
STPT(10)	2309069085364085921	0 2 30 32 60 62 90 92 120 122	-882470311566
TPT(14)	2309069104938369197	0 2 12 14 30 32 54 56 222 224 270 272 282 284	-862896028290
STPT(10)	2309069386080261197	0 2 30 32 42 44 54 56 84 86	-581754136290
TPT(14)	2309069398375529597	0 2 12 14 90 92 150 152 174 176 192 194 210 212	-569458867890
SPT(16)	2309069729425156921	0 40 58 72 136 178 192 208 270 286 300 342 406 420 438 478	-238409240566
SPT(16)	2309070072457762961	0 78 116 120 128 156 158 182 246 270 272 300 308 312 350 428	104623365474
STPT(10)	2309070718514266307	0 2 42 44 72 74 102 104 144 146	750679868820
SPT(16)	2309071816277204917	0 16 30 46 52 60 94 120 136 162 196 204 210 226 240 256	1848442807430
SPT(16)	2309071864927339049	0 18 20 30 32 152 158 200 222 264 270 390 392 402 404 422	1897092941562
SPT(16)	2309072018365658761	0 18 70 78 88 96 118 168 250 300 322 330 340 348 400 418	2050531261274