Prime p₀= 2566767655892067347 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: JayPi
db: batch=82, k=12, 2 10 2 10 2 4

SPT(16)	2566767012208910603	0 8 26 54 56 66 68 78 86 96 98 108 110 138 156 164	-643683156744
SPT(16)	2566767218671087613	0 26 44 48 60 80 104 114 140 150 174 194 206 210 228 254	-437220979734
STPT(10)	2566767246434209067	0 2 12 14 72 74 132 134 144 146	-409457858280
SPT(16)	2566767459235003909	0 22 30 40 70 100 108 114 118 124 132 162 192 202 210 232	-196657063438
SPT(16)	2566767556951323331	0 58 60 88 168 190 196 198 280 282 288 310 390 418 420 478	-98940744016
SPT(16)	2566767633755063261	0 6 12 50 68 92 116 120 158 162 186 210 228 266 272 278	-22137004086
SPT(16)	2566767802220280787	0 36 90 102 120 154 160 172 174 186 192 226 244 256 310 346	146328213440
STPT(10)	2566768624416468089	0 2 48 50 60 62 72 74 120 122	968524400742
STPT(10)	2566768757496294191	0 2 36 38 78 80 120 122 156 158	1101604226844
SPT(16)	2566768922261374763	0 20 36 48 84 86 104 126 128 150 168 170 206 218 234 254	1266369307416
SPT(16)	2566768965732929537	0 60 62 72 104 110 144 156 170 182 216 222 254 264 266 326	1309840862190