Prime p₀= 2565147726335427281 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 136 2 16 2 22 2 16 2 136 2 (?)
a_n: 0 2 138 140 156 158 180 182 198 200 336 338
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: 338
Found by: Penguin
db: batch=82, k=12, 2 136 2 16 2 22

STPT(10)	2565147194874414251	0 2 6 8 48 50 90 92 96 98	-531461013030
SPT(16)	2565147264957007279	0 28 40 52 54 64 82 90 112 120 138 148 150 162 174 202	-461378420002
STPT(10)	2565147279111245207	0 2 30 32 42 44 54 56 84 86	-447224182074
SPT(16)	2565147295334120701	0 22 58 66 138 162 166 178 210 222 226 250 322 330 366 388	-431001306580
STPT(10)	2565147509499710921	0 2 36 38 78 80 120 122 156 158	-216835716360
SPT(16)	2565147563524518701	0 2 60 66 72 128 170 176 192 198 240 296 302 308 366 368	-162810908580
STPT(10)	2565148008858848849	0 2 18 20 60 62 102 104 120 122	282523421568
STPT(10)	2565148757238947681	0 2 6 8 48 50 90 92 96 98	1030903520400
SPT(16)	2565148920628826869	0 12 52 72 88 102 138 154 168 184 220 234 250 270 310 322	1194293399588
TPT(14)	2565149181107043077	0 2 30 32 54 56 84 86 150 152 162 164 222 224	1454771615796
STPT(10)	2565149698856643161	0 2 6 8 48 50 90 92 96 98	1972521215880