Prime p₀= 868021081397088737 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: scrap
db: batch=73, k=10, 2 22 2 16 2

SPT(16)	868020415502634167	0 2 44 56 102 140 144 156 350 362 366 404 450 462 504 506	-665894454570
SPT(16)	868020478396698727	0 22 36 70 90 112 150 172 174 196 234 256 276 310 324 346	-603000390010
SPT(16)	868020575822235419	0 38 90 110 122 128 150 180 290 320 342 348 360 380 432 470	-505574853318
STPT(10)	868020603636310181	0 2 30 32 78 80 126 128 156 158	-477760778556
STPT(10)	868020718905145997	0 2 42 44 72 74 102 104 144 146	-362491942740
SPT(16)	868020811723031419	0 18 22 48 60 84 148 160 222 234 298 322 334 360 364 382	-269674057318
STPT(10)	868021151935303967	0 2 12 14 42 44 72 74 84 86	70538215230
STPT(10)	868021255882302419	0 2 18 20 30 32 42 44 60 62	174485213682
SPT(16)	868021296491875457	0 2 12 44 92 176 192 194 222 224 240 324 372 404 414 416	215094786720
TPT(14)	868021698025277039	0 2 60 62 138 140 168 170 180 182 192 194 252 254	616628188302
SPT(16)	868022129097886447	0 16 46 60 112 136 142 156 196 210 216 240 292 306 336 352	1047700797710