Prime p₀= 2565150897063231599 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)	2565148920628826869	0 12 52 72 88 102 138 154 168 184 220 234 250 270 310 322	-1976434404730
TPT(14)	2565149181107043077	0 2 30 32 54 56 84 86 150 152 162 164 222 224	-1715956188522
STPT(10)	2565149698856643161	0 2 6 8 48 50 90 92 96 98	-1198206588438
STPT(10)	2565149872628437571	0 2 36 38 78 80 120 122 156 158	-1024434794028
TPT(14)	2565150161978282951	0 2 18 20 78 80 156 158 216 218 228 230 336 338	-735084948648
STPT(10)	2565150350563205159	0 2 18 20 30 32 42 44 60 62	-546500026440
STPT(10)	2565151304338729817	0 2 12 14 42 44 72 74 84 86	407275498218
STPT(10)	2565151938451159199	0 2 18 20 30 32 42 44 60 62	1041387927600
SPT(13)	2565151974092813641	0 6 72 90 96 120 126 132 156 162 180 246 252	1077029582042
SPT(16)	2565152348216403551	0 50 56 60 110 116 138 158 240 260 282 288 338 342 348 398	1451153171952
SPT(16)	2565152446360201111	0 12 16 22 30 42 82 88 120 126 166 178 186 192 196 208	1549296969512