Prime p₀= 4387438297974166847 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: [SG]KidDoesCrunch
db: batch=85, k=10, 2 22 2 16 2

SPT(16)	4387437232750072343	0 20 30 56 66 90 96 104 156 164 170 194 204 230 240 260	-1065224094504
STPT(10)	4387437259136246669	0 2 12 14 90 92 168 170 180 182	-1038837920178
STPT(10)	4387437465602475839	0 2 18 20 60 62 102 104 120 122	-832371691008
STPT(10)	4387437660029766161	0 2 30 32 120 122 210 212 240 242	-637944400686
SPT(16)	4387437998002676317	0 22 42 52 70 100 150 172 210 232 282 312 330 340 360 382	-299971490530
STPT(10)	4387438286398504061	0 2 6 8 48 50 90 92 96 98	-11575662786
SPT(16)	4387438335613653571	0 16 42 96 108 172 192 228 250 286 306 370 382 436 462 478	37639486724
TPT(14)	4387438473026550629	0 2 48 50 78 80 198 200 240 242 288 290 312 314	175052383782
STPT(10)	4387438736427519467	0 2 30 32 60 62 90 92 120 122	438453352620
SPT(16)	4387438928227770263	0 38 50 80 84 104 140 168 170 198 234 254 258 288 300 338	630253603416
STPT(12)	4387438940596697939	0 2 18 20 42 44 48 50 72 74 90 92	642622531092