Prime p₀= 4404371637167251637 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 84 86
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: 86
Found by: Conan
db: batch=85, k=10, 2 28 2 10 2

SPT(16)	4404370787591224819	0 4 40 90 108 130 162 174 208 220 252 274 292 342 378 382	-849576026818
STPT(10)	4404370990888880951	0 2 30 32 60 62 90 92 120 122	-646278370686
STPT(10)	4404371196072759017	0 2 30 32 42 44 54 56 84 86	-441094492620
STPT(16)	4404371295990820157	0 2 12 14 54 56 84 86 150 152 180 182 222 224 234 236	-341176431480
TPT(16)	4404371295990820157	0 2 12 14 54 56 84 86 150 152 180 182 222 224 234 236	-341176431480
SPT(16)	4404371295990820157	0 2 12 14 54 56 84 86 150 152 180 182 222 224 234 236	-341176431480
STPT(10)	4404372001189209821	0 2 36 38 78 80 120 122 156 158	364021958184
SPT(16)	4404372088292662127	0 24 126 134 162 182 222 230 306 314 354 374 402 410 512 536	451125410490
STPT(10)	4404372092210502077	0 2 30 32 42 44 54 56 84 86	455043250440
SPT(16)	4404372274077636901	0 6 22 46 60 66 126 160 162 196 256 262 276 300 316 322	636910385264
STPT(10)	4404373667357903357	0 2 24 26 42 44 60 62 84 86	2030190651720