Prime p₀= 768065394126620921 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 34 2 10 2 28 2 10 2 34 2 (?)
a_n: 0 2 36 38 48 50 78 80 90 92 126 128
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: 128
Found by: GLeeM
db: batch=73, k=12, 2 34 2 10 2 28

SPT(16)	768064271969198177	0 30 72 84 114 140 182 212 234 264 306 332 362 374 416 446	-1122157422744
SPT(16)	768064813436313551	0 42 48 60 68 72 78 98 132 152 158 162 170 182 188 230	-580690307370
SPT(16)	768064902897018383	0 20 30 44 86 126 174 200 324 350 398 438 480 494 504 524	-491229602538
SPT(16)	768065172764224163	0 6 36 38 78 98 110 156 188 234 246 266 306 308 338 344	-221362396758
SPT(16)	768065301539023921	0 16 60 72 108 196 208 222 226 240 252 340 376 388 432 448	-92587597000
STPT(10)	768065348051204657	0 2 24 26 42 44 60 62 84 86	-46075416264
STPT(10)	768065408547044519	0 2 18 20 30 32 42 44 60 62	14420423598
STPT(10)	768065447042260361	0 2 36 38 78 80 120 122 156 158	52915639440
STPT(10)	768065454059906381	0 2 36 38 78 80 120 122 156 158	59933285460
SPT(16)	768065920017863227	0 4 10 34 40 54 66 94 126 154 166 180 186 210 216 220	525891242306
SPT(16)	768066299207409193	0 18 54 66 88 118 124 136 168 180 186 216 238 250 286 304	905080788272