Prime p₀= 959597398445425589 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 34 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 78 80 108 110 120 122
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: 122
Found by: HenkM
db: batch=76, k=12, 2 10 2 28 2 34

SPT(16)	959596136865163159	0 10 22 52 118 130 168 190 192 214 252 264 330 360 372 382	-1261580262430
TPT(14)	959596672467905741	0 2 36 38 78 80 90 92 276 278 318 320 390 392	-725977519848
SPT(16)	959596773668080591	0 42 66 102 112 168 180 196 252 268 280 336 346 382 406 448	-624777344998
SPT(16)	959597030363272723	0 24 36 70 78 94 114 198 226 310 330 346 354 388 400 424	-368082152866
TPT(14)	959597226305397971	0 2 30 32 96 98 168 170 210 212 300 302 420 422	-172140027618
TPT(14)	959597398445425547	0 2 42 44 54 56 84 86 120 122 150 152 162 164	-42
SPT(16)	959597576129478233	0 6 24 38 50 56 84 126 188 230 258 264 276 290 308 314	177684052644
SPT(16)	959597625917329283	0 26 54 80 96 108 120 140 234 254 266 278 294 320 348 374	227471903694
TPT(14)	959598634894897379	0 2 18 20 30 32 72 74 132 134 180 182 222 224	1236449471790
SPT(16)	959599067386493081	0 38 60 66 80 120 122 140 168 186 188 228 242 248 270 308	1668941067492
STPT(10)	959599107382612391	0 2 30 32 60 62 90 92 120 122	1708937186802