Prime p₀= 2377726226054459741 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 46 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 108 110 138 140 168 170
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: 170
Found by: Landjunge
db: batch=81, k=12, 2 28 2 28 2 46

SPT(16)	2377725274931454611	0 8 42 50 56 66 72 78 80 86 92 102 108 116 150 158	-951123005130
SPT(16)	2377725561362123263	0 16 30 36 70 76 120 148 168 196 240 246 280 286 300 316	-664692336478
SPT(13)	2377725672270518497	0 6 30 90 96 120 126 132 156 162 222 246 252	-553783941244
SPT(16)	2377725781713067459	0 10 48 72 148 160 190 214 258 282 312 324 400 424 462 472	-444341392282
STPT(10)	2377726064977536809	0 2 48 50 90 92 132 134 180 182	-161076922932
STPT(10)	2377726153201058279	0 2 42 44 90 92 138 140 180 182	-72853401462
SPT(16)	2377726686728261387	0 44 54 72 80 84 150 194 252 296 362 366 374 392 402 446	460673801646
SPT(16)	2377727147351242987	0 6 46 94 130 136 150 154 156 160 174 180 216 264 304 310	921296783246
STPT(10)	2377727349186248177	0 2 30 32 42 44 54 56 84 86	1123131788436
SPT(16)	2377727591927501573	0 50 78 96 110 134 146 156 158 168 180 204 218 236 264 314	1365873041832
STPT(10)	2377727633455533407	0 2 42 44 72 74 102 104 144 146	1407401073666