Prime p₀= 2589592527334312469 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 16 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 48 50 60 62
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: 62
Found by: JayPi
db: batch=82, k=10, 2 10 2 16 2

SPT(16)	2589591391415524579	0 10 52 88 90 114 130 132 220 222 238 262 264 300 342 352	-1135918787890
SPT(16)	2589591512739627299	0 2 14 24 68 92 164 168 194 198 270 294 338 348 360 362	-1014594685170
SPT(16)	2589591630653509847	0 84 110 120 134 144 150 180 206 236 242 252 266 276 302 386	-896680802622
SPT(16)	2589591740699288011	0 12 42 52 96 142 166 192 280 306 330 376 420 430 460 472	-786635024458
STPT(10)	2589591802401667487	0 2 54 56 72 74 90 92 144 146	-724932644982
SPT(16)	2589592316402771857	0 16 52 66 102 114 130 132 154 156 172 184 220 234 270 286	-210931540612
STPT(10)	2589592736486533121	0 2 36 38 78 80 120 122 156 158	209152220652
SPT(18)	2589592970710397909	0 8 14 48 132 140 158 180 200 252 272 294 312 320 404 438 444 452	443376085440
SPT(16)	2589593285353788341	0 18 62 90 150 162 182 188 222 228 248 260 320 348 392 410	758019475872
TPT(14)	2589593895705635591	0 2 90 92 108 110 120 122 246 248 258 260 318 320	1368371323122
TPT(14)	2589593909079007319	0 2 30 32 60 62 102 104 192 194 228 230 282 284	1381744694850