Prime p₀= 2567334666074195999 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 40 2 40 2 16 2 (?)
a_n: 0 2 18 20 60 62 102 104 120 122
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 122
Found by: SEARCHER
db: batch=82, k=10, 2 16 2 40 2

SPT(16)	2567333537423768177	0 26 50 60 72 84 96 114 122 140 152 164 176 186 210 236	-1128650427822
SPT(18)	2567333677728052001	0 6 20 32 42 60 66 146 150 182 186 266 272 290 300 312 326 332	-988346143998
SPT(16)	2567333721021351757	0 24 34 66 76 82 124 156 220 252 294 300 310 342 352 376	-945052844242
SPT(16)	2567333862805792711	0 30 66 82 138 142 148 208 210 270 276 280 336 352 388 418	-803268403288
TPT(14)	2567333980802682941	0 2 78 80 90 92 126 128 210 212 246 248 300 302	-685271513058
STPT(10)	2567334028107381719	0 2 42 44 90 92 138 140 180 182	-637966814280
SPT(16)	2567334680231163421	0 46 78 102 120 130 132 148 150 166 168 178 196 220 252 298	14156967422
STPT(10)	2567335237882679879	0 2 18 20 30 32 42 44 60 62	571808483880
SPT(16)	2567335305712316911	0 30 46 66 70 72 186 226 312 352 466 468 472 492 508 538	639638120912
STPT(10)	2567335603563157949	0 2 18 20 30 32 42 44 60 62	937488961950
STPT(10)	2567336377078571249	0 2 48 50 90 92 132 134 180 182	1711004375250