Prime p₀= 2313126296231691737 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 22 2 4 2 22 2 4 2 22 2 (?)
a_n: 0 2 24 26 30 32 54 56 60 62 84 86
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: 86
Found by: vinn@[CNT]
db: batch=81, k=12, 2 22 2 4 2 22

SPT(16)	2313124876627821467	0 2 32 54 80 96 110 116 150 156 170 186 212 234 264 266	-1419603870270
SPT(16)	2313124961058467951	0 6 36 50 62 96 120 132 170 182 206 240 252 266 296 302	-1335173223786
SPT(16)	2313125017959668467	0 34 60 66 130 154 240 256 384 400 486 510 574 580 606 640	-1278272023270
SPT(16)	2313125944878357971	0 20 48 90 96 116 300 312 356 368 552 572 578 620 648 668	-351353333766
SPT(20)	2313125946200821639	0 12 40 42 52 54 72 94 108 132 160 184 198 220 238 240 250 252 280 292	-350030870098
SPT(16)	2313126219506703641	0 20 32 50 78 122 176 210 308 342 396 440 468 486 498 518	-76724988096
SPT(16)	2313126520308634973	0 50 66 96 98 108 134 138 176 180 206 216 218 248 264 314	224076943236
SPT(13)	2313127301743340387	0 6 42 90 96 120 126 132 156 162 210 246 252	1005511648650
STPT(10)	2313127371475757561	0 2 6 8 48 50 90 92 96 98	1075244065824
STPT(10)	2313127448197533239	0 2 18 20 30 32 42 44 60 62	1151965841502
TPT(14)	2313128232094596647	0 2 42 44 150 152 162 164 264 266 300 302 330 332	1935862904910