Prime p₀= 2162569998527630381 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 64 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 126 128 156 158 186 188
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: 188
Found by: Landjunge
db: batch=81, k=12, 2 28 2 28 2 64

SPT(16)	2162568435097866277	0 42 52 54 60 76 82 94 132 144 150 166 172 174 184 226	-1563429764104
STPT(10)	2162568618270685451	0 2 30 32 78 80 126 128 156 158	-1380256944930
TPT(14)	2162568684459121661	0 2 48 50 90 92 186 188 228 230 246 248 288 290	-1314068508720
STPT(10)	2162569351825399721	0 2 96 98 138 140 180 182 276 278	-646702230660
STPT(10)	2162569390963948607	0 2 90 92 132 134 174 176 264 266	-607563681774
STPT(10)	2162569655290087187	0 2 60 62 72 74 84 86 144 146	-343237543194
SPT(16)	2162570225095799357	0 44 56 104 150 156 216 252 314 350 410 416 462 510 522 566	226568168976
SPT(16)	2162570466124200859	0 12 24 48 84 94 108 124 138 154 168 178 214 238 250 262	467596570478
SPT(16)	2162570558292374917	0 36 42 60 64 96 130 144 172 186 220 252 256 274 280 316	559764744536
STPT(10)	2162570760036978407	0 2 30 32 42 44 54 56 84 86	761509348026
TPT(14)	2162570788623328397	0 2 30 32 54 56 144 146 150 152 210 212 264 266	790095698016