Prime p₀= 2568664267823359169 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 46 2 10 2 10 2 46 2 (?)
a_n: 0 2 48 50 60 62 72 74 120 122
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: Roadranner
db: batch=82, k=10, 2 46 2 10 2

SPT(16)	2568662960955270581	0 2 12 48 68 90 128 132 176 180 218 240 260 296 306 308	-1306868088588
SPT(16)	2568663133907082029	0 48 68 74 80 90 152 158 174 180 242 252 258 264 284 332	-1133916277140
STPT(10)	2568663346218520247	0 2 30 32 72 74 114 116 144 146	-921604838922
TPT(14)	2568663952070546609	0 2 12 14 42 44 102 104 108 110 180 182 222 224	-315752812560
STPT(10)	2568664144730454227	0 2 30 32 72 74 114 116 144 146	-123092904942
SPT(16)	2568664208764432577	0 2 50 66 102 134 192 242 294 344 402 434 470 486 534 536	-59058926592
SPT(16)	2568664311659085821	0 42 48 60 80 108 126 152 186 212 230 258 278 290 296 338	43835726652
STPT(10)	2568664509336743729	0 2 18 20 30 32 42 44 60 62	241513384560
STPT(10)	2568664883022453947	0 2 30 32 42 44 54 56 84 86	615199094778
STPT(10)	2568664920623465327	0 2 42 44 72 74 102 104 144 146	652800106158
TPT(14)	2568664968953467367	0 2 12 14 84 86 90 92 102 104 144 146 222 224	701130108198