Prime p₀= 2512825852437668231 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: Penguin
db: batch=82, k=12, 2 34 2 10 2 28

SPT(16)	2512825464082926259	0 18 70 72 82 88 108 204 298 394 414 420 430 432 484 502	-388354741972
STPT(10)	2512825522674018449	0 2 18 20 60 62 102 104 120 122	-329763649782
STPT(10)	2512825524585729839	0 2 12 14 90 92 168 170 180 182	-327851938392
SPT(16)	2512825560509532157	0 16 22 30 42 120 184 186 190 192 256 334 346 354 360 376	-291928136074
SPT(16)	2512825759520762003	0 26 48 50 86 180 236 240 314 318 374 468 504 506 528 554	-92916906228
STPT(10)	2512825840360539017	0 2 240 242 252 254 264 266 504 506	-12077129214
SPT(16)	2512826442893972371	0 48 106 112 118 160 162 202 216 256 258 300 306 312 370 418	590456304140
SPT(16)	2512826857513560359	0 14 18 38 44 78 104 114 134 144 170 204 210 230 234 248	1005075892128
SPT(16)	2512827117953795893	0 6 40 60 90 118 150 204 220 274 306 334 364 384 418 424	1265516127662
SPT(16)	2512827122421197941	0 28 52 78 100 108 118 130 258 270 280 288 310 336 360 388	1269983529710
SPT(16)	2512827525536010503	0 20 78 84 86 104 108 120 134 146 150 168 170 176 234 254	1673098342272