Prime p₀= 2723077614157418657 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)	2723076786667452161	0 18 20 36 116 150 200 228 248 276 326 360 440 456 458 476	-827489966496
TPT(14)	2723077024966054061	0 2 6 8 30 32 138 140 156 158 180 182 240 242	-589191364596
SPT(16)	2723077093714252553	0 6 14 38 50 56 104 108 116 120 168 174 186 210 218 224	-520443166104
SPT(16)	2723077118171596649	0 12 42 72 108 114 138 150 182 194 218 224 260 290 320 332	-495985822008
SPT(16)	2723077350996363817	0 22 24 54 60 100 124 162 172 210 234 274 280 310 312 334	-263161054840
SPT(16)	2723077565929194281	0 36 42 62 68 80 188 198 230 240 348 360 366 386 392 428	-48228224376
STPT(10)	2723078002995564827	0 2 30 32 42 44 54 56 84 86	388838146170
STPT(10)	2723078675396953187	0 2 30 32 42 44 54 56 84 86	1061239534530
SPT(16)	2723078696121740161	0 22 36 76 100 130 150 210 262 322 342 372 396 436 450 472	1081964321504
SPT(16)	2723079224580528553	0 18 60 106 180 210 214 238 306 330 334 364 438 484 526 544	1610423109896
STPT(10)	2723079237414393587	0 2 30 32 72 74 114 116 144 146	1623256974930