Prime p₀= 3717731631875157077 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: Sphynx
db: batch=84, k=10, 2 22 2 16 2

SPT(16)	3717729635891769671	0 12 26 66 78 110 162 206 222 266 318 350 362 402 416 428	-1995983387406
STPT(10)	3717729780564492617	0 2 12 14 42 44 72 74 84 86	-1851310664460
SPT(16)	3717730196728309681	0 12 72 96 100 148 156 166 222 232 240 288 292 316 376 388	-1435146847396
SPT(16)	3717730571221613389	0 18 22 34 84 144 148 150 172 174 178 238 288 300 304 322	-1060653543688
STPT(10)	3717731152988929631	0 2 36 38 78 80 120 122 156 158	-478886227446
SPT(16)	3717731189351217977	0 12 26 44 54 86 96 110 156 170 180 212 222 240 254 266	-442523939100
SPT(16)	3717732064606390841	0 26 30 48 66 72 86 110 168 192 206 212 230 248 252 278	432731233764
SPT(16)	3717732084132515599	0 22 40 132 148 168 192 204 208 220 244 264 280 372 390 412	452257358522
SPT(16)	3717732204704445833	0 24 44 120 146 170 188 246 308 366 384 408 434 510 530 554	572829288756
STPT(10)	3717732280051856777	0 2 12 14 42 44 72 74 84 86	648176699700
SPT(16)	3717732307696910599	0 12 78 90 144 154 160 172 210 222 228 238 292 304 370 382	675821753522