Prime p₀= 2019567181151224799 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 34 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 78 80 108 110 120 122
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: 122
Found by: matsu_pl
db: batch=80, k=12, 2 10 2 28 2 34

SPT(16)	2019565441038368581	0 10 36 70 78 88 100 142 156 198 210 220 228 262 288 298	-1740112856218
SPT(16)	2019565463026759049	0 42 114 128 162 168 188 204 218 234 254 260 294 308 380 422	-1718124465750
STPT(10)	2019565633796922119	0 2 18 20 30 32 42 44 60 62	-1547354302680
SPT(16)	2019566086953729959	0 12 30 42 50 98 162 264 308 410 474 522 530 542 560 572	-1094197494840
SPT(16)	2019566126026949971	0 16 30 48 120 126 136 162 226 252 262 268 340 358 372 388	-1055124274828
STPT(10)	2019566144969871539	0 2 18 20 30 32 42 44 60 62	-1036181353260
SPT(16)	2019567194549764061	0 20 30 72 102 108 192 210 230 248 332 338 368 410 420 440	13398539262
SPT(16)	2019567235332900863	0 18 24 26 38 150 156 198 236 278 284 396 408 410 416 434	54181676064
SPT(16)	2019567346634552833	0 10 24 66 126 130 144 150 154 160 174 178 238 280 294 304	165483328034
SPT(16)	2019567411852586667	0 30 32 44 56 74 80 110 156 186 192 210 222 234 236 266	230701361868
SPT(16)	2019567763807412341	0 28 46 52 102 138 150 162 196 208 220 256 306 312 330 358	582656187542