Prime p₀= 800311999562361131 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 4 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 66 68 96 98 126 128
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: 128
Found by: jozef j
db: batch=73, k=12, 2 28 2 28 2 4

SPT(16)	800309758351791581	0 12 38 60 78 126 138 158 210 230 242 290 308 330 356 368	-2241210569550
STPT(10)	800310282096118637	0 2 30 32 42 44 54 56 84 86	-1717466242494
SPT(16)	800310825537368323	0 10 28 34 36 66 94 138 346 390 418 448 450 456 474 484	-1174024992808
STPT(10)	800310915532013537	0 2 210 212 222 224 234 236 444 446	-1084030347594
SPT(16)	800310924162655681	0 12 40 58 70 90 102 132 136 166 178 198 210 228 256 268	-1075399705450
STPT(10)	800310975118546607	0 2 42 44 72 74 102 104 144 146	-1024443814524
TPT(14)	800312869532888417	0 2 54 56 180 182 270 272 312 314 390 392 450 452	869970527286
SPT(16)	800313086014211059	0 30 42 58 72 82 94 138 154 198 210 220 234 250 262 292	1086451849928
SPT(16)	800313827941101349	0 10 22 28 42 72 78 108 142 172 178 208 222 228 240 250	1828378740218
SPT(16)	800313841258049731	0 16 30 60 72 90 106 118 240 252 268 286 298 328 342 358	1841695688600
STPT(10)	800313867297104057	0 2 42 44 72 74 102 104 144 146	1867734742926