Prime p₀= 1286508215145750587 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: Cruncher Pete
db: batch=77, k=10, 2 10 2 28 2

SPT(16)	1286505983517113399	0 134 144 164 248 260 284 294 308 318 342 354 438 458 468 602	-2231628637188
STPT(10)	1286506357167770267	0 2 42 44 72 74 102 104 144 146	-1857977980320
SPT(16)	1286506931809074541	0 40 52 70 76 82 96 130 132 166 180 186 192 210 222 262	-1283336676046
SPT(16)	1286507346668592383	0 24 30 44 48 84 104 258 290 444 464 500 504 518 524 548	-868477158204
STPT(10)	1286507768113870397	0 2 30 32 42 44 54 56 84 86	-447031880190
TPT(14)	1286507873353314047	0 2 120 122 144 146 174 176 270 272 324 326 450 452	-341792436540
STPT(10)	1286508235182493109	0 2 48 50 90 92 132 134 180 182	20036742522
SPT(16)	1286508258689752817	0 6 12 42 104 132 144 164 252 272 284 312 374 404 410 416	43544002230
SPT(16)	1286508374602550893	0 6 30 34 36 40 48 70 84 106 114 118 120 124 148 154	159456800306
SPT(16)	1286508627195405137	0 12 20 56 62 84 110 140 186 216 242 264 270 306 314 326	412049654550
STPT(10)	1286508739559743949	0 2 18 20 30 32 42 44 60 62	524413993362