Prime p₀= 4387502862469386761 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 40 2 40 2 4 2 (?)
a_n: 0 2 6 8 48 50 90 92 96 98
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: 98
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 4 2 40 2

SPT(16)	4387500411501825689	0 14 24 44 78 122 144 170 192 218 240 284 318 338 348 362	-2450967561072
SPT(16)	4387500447698018687	0 14 72 92 114 116 134 150 176 192 210 212 234 254 312 326	-2414771368074
SPT(16)	4387500744636647089	0 70 88 114 148 168 180 190 222 232 244 264 298 324 342 412	-2117832739672
STPT(10)	4387500978425261777	0 2 90 92 150 152 210 212 300 302	-1884044124984
SPT(16)	4387501228682631863	0 20 30 44 56 90 96 138 146 188 194 228 240 254 264 284	-1633786754898
STPT(10)	4387501900420013729	0 2 48 50 90 92 132 134 180 182	-962049373032
STPT(10)	4387503494646759959	0 2 42 44 90 92 138 140 180 182	632177373198
SPT(16)	4387503687291773413	0 30 46 54 78 96 154 156 178 180 238 256 280 288 304 334	824822386652
SPT(16)	4387503732681102893	0 90 104 114 116 150 168 234 290 356 374 408 410 420 434 524	870211716132
SPT(16)	4387504089218955751	0 12 16 28 36 40 46 48 70 72 78 82 90 102 106 118	1226749568990
STPT(10)	4387504623411344387	0 2 30 32 42 44 54 56 84 86	1760941957626