Prime p₀= 2564425074590461517 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: RFGuy_KCCO
db: batch=82, k=12, 2 10 2 10 2 4

SPT(16)	2564423608318678699	0 10 22 52 60 130 150 154 168 172 192 262 270 300 312 322	-1466271782818
STPT(10)	2564423695729954691	0 2 6 8 48 50 90 92 96 98	-1378860506826
SPT(16)	2564423741946841069	0 10 150 168 184 190 204 232 270 298 312 318 334 352 492 502	-1332643620448
TPT(14)	2564423946790527671	0 2 48 50 66 68 246 248 300 302 306 308 348 350	-1127799933846
TPT(14)	2564424474187911689	0 2 12 14 72 74 168 170 228 230 258 260 408 410	-600402549828
TPT(14)	2564424918497225891	0 2 30 32 156 158 240 242 330 332 396 398 546 548	-156093235626
STPT(10)	2564426225583175739	0 2 30 32 60 62 90 92 120 122	1150992714222
STPT(10)	2564426326508849651	0 2 30 32 60 62 90 92 120 122	1251918388134
SPT(16)	2564427036374359711	0 16 46 48 78 88 126 130 216 220 258 268 298 300 330 346	1961783898194
SPT(16)	2564427210905454403	0 36 46 48 54 64 130 166 168 204 270 280 286 288 298 334	2136314992886
SPT(16)	2564427228889371607	0 12 40 46 84 100 124 126 130 132 156 172 210 216 244 256	2154298910090