Prime p₀= 1117627889898769829 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 40 2 34 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 108 110 150 152 180 182
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: 182
Found by: crashtech
db: batch=76, k=12, 2 28 2 40 2 34

SPT(16)	1117626916820550527	0 2 24 30 42 56 72 174 182 284 300 314 326 332 354 356	-973078219302
STPT(10)	1117627514258517971	0 2 36 38 78 80 120 122 156 158	-375640251858
STPT(10)	1117627533471201587	0 2 72 74 102 104 132 134 204 206	-356427568242
STPT(10)	1117627543094769401	0 2 30 32 60 62 90 92 120 122	-346804000428
STPT(10)	1117627555960007669	0 2 90 92 150 152 210 212 300 302	-333938762160
STPT(10)	1117627863405407111	0 2 6 8 18 20 30 32 36 38	-26493362718
SPT(16)	1117628106194804261	0 12 26 78 122 126 150 206 252 308 332 336 380 432 446 458	216296034432
SPT(16)	1117628136159678167	0 30 96 110 150 192 230 272 300 342 380 422 462 476 542 572	246260908338
STPT(10)	1117628141071447301	0 2 6 8 18 20 30 32 36 38	251172677472
SPT(16)	1117628167654294979	0 18 42 68 102 134 210 222 260 272 348 380 414 440 464 482	277755525150
SPT(16)	1117628190867584743	0 34 36 90 118 130 138 144 190 196 204 216 244 298 300 334	300968814914