Prime p₀= 810169507819336937 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 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: GLeeM
db: batch=73, k=10, 2 22 2 16 2

SPT(20)	810168545312799481	0 70 72 78 118 160 172 180 222 238 300 316 358 366 378 420 460 466 468 538	-962506537456
SPT(16)	810168645079089083	0 36 56 60 120 186 204 210 230 236 254 320 380 384 404 440	-862740247854
SPT(16)	810169200634715833	0 10 18 28 30 58 64 70 108 114 120 148 150 160 168 178	-307184621104
STPT(10)	810169235317522139	0 2 12 14 90 92 168 170 180 182	-272501814798
SPT(16)	810169250230805813	0 6 14 18 78 110 134 140 144 150 174 206 266 270 278 284	-257588531124
STPT(10)	810169340033707427	0 2 12 14 72 74 132 134 144 146	-167785629510
STPT(10)	810169512607381007	0 2 12 14 72 74 132 134 144 146	4788044070
STPT(10)	810169533342861059	0 2 18 20 30 32 42 44 60 62	25523524122
TPT(14)	810169708548205301	0 2 18 20 30 32 90 92 156 158 168 170 228 230	200728868364
SPT(16)	810169918135507613	0 38 56 78 134 180 206 210 344 348 374 420 476 498 516 554	410316170676
STPT(10)	810170280396886889	0 2 18 20 30 32 42 44 60 62	772577549952