Prime p₀= 2589998622648459947 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: Roadranner
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2589996195529759099	0 28 30 48 52 84 88 94 108 114 118 150 154 172 174 202	-2427118700848
SPT(16)	2589996541141470239	0 18 32 50 72 78 104 114 188 198 224 230 252 270 284 302	-2081506989708
SPT(16)	2589997111832601137	0 14 20 50 102 120 164 176 240 252 296 314 366 396 402 416	-1510815858810
SPT(16)	2589997279804631819	0 30 42 48 62 104 140 150 152 162 198 240 254 260 272 302	-1342843828128
SPT(16)	2589997813663919941	0 42 46 52 66 100 112 150 178 216 228 262 276 282 286 328	-808984540006
STPT(10)	2589998009736633017	0 2 30 32 42 44 54 56 84 86	-612911826930
STPT(10)	2589999211576046321	0 2 6 8 18 20 30 32 36 38	588927586374
SPT(16)	2589999457210541023	0 18 30 64 96 148 208 214 240 246 306 358 390 424 436 454	834562081076
TPT(14)	2590000189261617329	0 2 30 32 150 152 168 170 198 200 240 242 372 374	1566613157382
TPT(14)	2590000280478921239	0 2 12 14 18 20 72 74 150 152 222 224 252 254	1657830461292
SPT(16)	2590000345242948013	0 24 54 60 120 136 166 210 214 258 288 304 364 370 400 424	1722594488066