Prime p₀= 2565249048230941691 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: JayPi
db: batch=82, k=12, 2 34 2 10 2 28

SPT(16)	2565245460931331977	0 16 42 60 82 84 96 172 234 310 322 324 346 364 390 406	-3587299609714
STPT(12)	2565245779996931747	0 2 42 44 60 62 84 86 102 104 144 146	-3268234009944
STPT(10)	2565246803094219071	0 2 36 38 78 80 120 122 156 158	-2245136722620
SPT(16)	2565247077793625749	0 12 58 108 112 118 142 168 184 210 234 240 244 294 340 352	-1970437315942
SPT(16)	2565247195657733989	0 42 48 58 84 94 132 138 154 160 198 208 234 244 250 292	-1852573207702
STPT(10)	2565248066500226477	0 2 30 32 42 44 54 56 84 86	-981730715214
STPT(10)	2565249091029344021	0 2 30 32 78 80 126 128 156 158	42798402330
SPT(16)	2565249356143614947	0 60 86 102 122 126 146 204 212 270 290 294 314 330 356 416	307912673256
STPT(10)	2565249389907065987	0 2 30 32 72 74 114 116 144 146	341676124296
STPT(10)	2565249461793247037	0 2 54 56 72 74 90 92 144 146	413562305346
STPT(10)	2565249624504327557	0 2 24 26 42 44 60 62 84 86	576273385866