Prime p₀= 2308992854125352567 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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: Landjunge
db: batch=81, k=10, 2 10 2 28 2

SPT(16)	2308990372097923061	0 30 32 78 86 158 188 218 240 270 300 372 380 426 428 458	-2482027429506
STPT(10)	2308990666995915587	0 2 24 26 42 44 60 62 84 86	-2187129436980
STPT(12)	2308990673093757929	0 2 12 14 42 44 48 50 78 80 90 92	-2181031594638
SPT(16)	2308991451340603277	0 6 56 80 86 96 146 150 212 216 266 276 282 306 356 362	-1402784749290
STPT(10)	2308991817728923487	0 2 30 32 42 44 54 56 84 86	-1036396429080
TPT(14)	2308992133632338771	0 2 36 38 126 128 138 140 180 182 246 248 288 290	-720493013796
STPT(10)	2308992936578339327	0 2 30 32 42 44 54 56 84 86	82452986760
SPT(16)	2308992971094502541	0 30 32 38 56 116 170 212 246 288 342 402 420 426 428 458	116969149974
STPT(10)	2308993074221683697	0 2 12 14 42 44 72 74 84 86	220096331130
SPT(16)	2308993122367528067	0 14 56 74 102 126 146 170 186 210 230 254 282 300 342 356	268242175500
SPT(16)	2308993161163452391	0 12 40 42 90 180 222 228 280 286 328 418 466 468 496 508	307038099824