Prime p₀= 1976099199752586917 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 82 2 28 2 34 2 28 2 82 2 (?)
a_n: 0 2 84 86 114 116 150 152 180 182 264 266
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: 266
Found by: Landjunge
db: batch=80, k=12, 2 82 2 28 2 34

SPT(16)	1976097938411217199	0 18 24 34 90 94 108 138 160 190 204 208 264 274 280 298	-1261341369718
SPT(16)	1976098413215334607	0 72 84 114 156 196 210 216 220 226 240 280 322 352 364 436	-786537252310
SPT(16)	1976098500431167741	0 6 72 82 100 126 226 228 250 252 352 378 396 406 472 478	-699321419176
STPT(10)	1976098668572751509	0 2 42 44 90 92 138 140 180 182	-531179835408
STPT(10)	1976098860943422167	0 2 30 32 42 44 54 56 84 86	-338809164750
SPT(16)	1976098926925365071	0 12 90 120 162 188 198 230 498 530 540 566 608 638 716 728	-272827221846
TPT(14)	1976099280113631767	0 2 12 14 24 26 84 86 90 92 150 152 222 224	80361044850
SPT(16)	1976099331861808663	0 34 58 108 136 144 154 168 286 300 310 318 346 396 420 454	132109221746
TPT(14)	1976099546255355047	0 2 72 74 90 92 102 104 174 176 294 296 300 302	346502768130
SPT(16)	1976099596733037103	0 30 34 48 58 60 100 130 168 198 238 240 250 264 268 298	396980450186
STPT(10)	1976099723255657117	0 2 24 26 42 44 60 62 84 86	523503070200