Prime p₀= 2562779696661898619 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 4 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 48 50 78 80 90 92
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: 92
Found by: JayPi
db: batch=82, k=12, 2 10 2 28 2 4

SPT(16)	2562778284741910979	0 20 42 50 84 132 150 188 204 242 260 308 342 350 372 392	-1411919987640
TPT(14)	2562778584873311951	0 2 108 110 150 152 186 188 306 308 378 380 396 398	-1111788586668
SPT(16)	2562778736966907409	0 48 82 88 114 130 144 174 208 238 252 268 294 300 334 382	-959694991210
SPT(16)	2562778776809606287	0 66 70 72 84 160 196 226 270 300 336 412 424 426 430 496	-919852292332
SPT(16)	2562778935650316937	0 10 54 136 144 156 184 196 210 222 250 262 270 352 396 406	-761011581682
SPT(16)	2562779285783198719	0 18 24 48 90 100 132 174 178 220 252 262 304 328 334 352	-410878699900
SPT(16)	2562780072281038783	0 18 40 60 120 144 160 174 244 258 274 298 358 378 400 418	375619140164
STPT(10)	2562780134031624719	0 2 42 44 60 62 78 80 120 122	437369726100
SPT(16)	2562780168916973009	0 50 72 102 120 182 188 218 222 252 258 320 338 368 390 440	472255074390
STPT(10)	2562780232564941197	0 2 30 32 42 44 54 56 84 86	535903042578
TPT(14)	2562780296831172989	0 2 18 20 48 50 60 62 72 74 180 182 198 200	600169274370