Prime p₀= 2568386708757678449 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 16 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 60 62 90 92 102 104
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: 104
Found by: JayPi
db: batch=82, k=12, 2 10 2 28 2 16

SPT(16)	2568386068575845407	0 10 22 24 52 130 204 310 366 472 546 624 652 654 666 676	-640181833042
SPT(16)	2568386365472456167	0 22 30 34 90 94 114 190 204 280 300 304 360 364 372 394	-343285222282
STPT(10)	2568386611669503797	0 2 30 32 42 44 54 56 84 86	-97088174652
TPT(16)	2568386673458080331	0 2 6 8 36 38 48 50 96 98 108 110 138 140 150 152	-35299598118
STPT(12)	2568386673458080337	0 2 30 32 42 44 90 92 102 104 132 134	-35299598112
SPT(16)	2568386698595209727	0 2 36 44 54 92 96 126 140 170 174 212 222 230 264 266	-10162468722
SPT(16)	2568386914485052709	0 2 20 48 60 72 152 180 200 228 308 320 332 360 378 380	205727374260
STPT(10)	2568386957464480049	0 2 18 20 60 62 102 104 120 122	248706801600
STPT(10)	2568387001706670887	0 2 30 32 42 44 54 56 84 86	292948992438
SPT(16)	2568387099733786339	0 4 54 82 88 130 142 154 198 210 222 264 270 298 348 352	390976107890
SPT(16)	2568387134668947833	0 14 38 66 126 138 150 156 218 224 236 248 308 336 360 374	425911269384