Prime p₀= 2380676105597619587 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 40 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 102 104 132 134 162 164
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: 164
Found by: Landjunge
db: batch=81, k=12, 2 28 2 28 2 40

SPT(16)	2380673410275208481	0 20 56 60 132 146 180 182 366 368 402 416 488 492 528 548	-2695322411106
SPT(18)	2380673530235888477	0 24 32 42 84 120 140 186 204 212 230 276 296 332 374 384 392 416	-2575361731110
SPT(16)	2380674085399316827	0 30 64 96 112 120 142 150 196 204 226 234 250 282 316 346	-2020198302760
STPT(10)	2380674270476059799	0 2 42 44 90 92 138 140 180 182	-1835121559788
SPT(16)	2380674776761525393	0 24 76 88 94 120 154 168 196 210 244 270 276 288 340 364	-1328836094194
SPT(16)	2380675281992255197	0 22 52 54 66 94 126 136 180 190 222 250 262 264 294 316	-823605364390
SPT(16)	2380676160167277823	0 48 54 60 166 180 190 204 250 264 274 288 394 400 406 454	54569658236
STPT(10)	2380676238455858669	0 2 18 20 30 32 42 44 60 62	132858239082
SPT(16)	2380676279738560439	0 12 30 62 72 102 164 198 224 258 320 350 360 392 410 422	174140940852
SPT(16)	2380676472624457291	0 22 30 36 60 76 88 102 226 240 252 268 292 298 306 328	367026837704
SPT(16)	2380676672411148311	0 26 62 72 96 140 188 210 308 330 378 422 446 456 492 518	566813528724