Prime p₀= 1296905925519746207 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: Cruncher Pete
db: batch=77, k=12, 2 10 2 10 2 4

SPT(16)	1296905026474252193	0 20 56 60 84 104 126 140 150 164 186 206 230 234 270 290	-899045494014
STPT(10)	1296905177885648699	0 2 18 20 30 32 42 44 60 62	-747634097508
SPT(16)	1296905530983693859	0 70 78 88 100 120 198 250 288 340 418 438 450 460 468 538	-394536052348
STPT(10)	1296905540222258171	0 2 6 8 18 20 30 32 36 38	-385297488036
SPT(16)	1296905769028641913	0 10 16 30 40 58 78 136 378 436 456 474 484 498 504 514	-156491104294
SPT(16)	1296905781899559641	0 18 32 78 80 98 102 108 110 116 120 138 140 186 200 218	-143620186566
TPT(14)	1296905925519746207	0 2 12 14 24 26 30 32 42 44 54 56 180 182	0
STPT(10)	1296906015364725707	0 2 30 32 42 44 54 56 84 86	89844979500
SPT(16)	1296906144342901451	0 2 20 56 60 62 72 86 102 116 126 128 132 168 186 188	218823155244
STPT(10)	1296906457997520707	0 2 30 32 42 44 54 56 84 86	532477774500
STPT(10)	1296906558223099007	0 2 30 32 60 62 90 92 120 122	632703352800