Prime p₀= 2515171553361733727 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 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: [AF>Linux]Rogue 9
db: batch=82, k=10, 2 22 2 16 2

SPT(16)	2515169797668072833	0 56 60 158 170 324 434 456 458 480 590 744 756 854 858 914	-1755693660894
SPT(16)	2515169993390662423	0 6 34 60 78 84 88 100 144 156 160 166 184 210 238 244	-1559971071304
SPT(16)	2515170135308506919	0 12 20 60 74 84 144 150 182 188 248 258 272 312 320 332	-1418053226808
STPT(10)	2515170399340106537	0 2 30 32 42 44 54 56 84 86	-1154021627190
SPT(16)	2515170727504804543	0 18 40 66 70 186 214 256 258 300 328 444 448 474 496 514	-825856929184
STPT(12)	2515171114016086187	0 2 30 32 60 62 72 74 102 104 132 134	-439345647540
SPT(16)	2515172562283871531	0 32 42 56 60 68 72 110 198 236 240 248 252 266 276 308	1008922137804
SPT(13)	2515172933598790103	0 6 18 48 66 90 108 126 150 168 198 210 216	1380237056376
TPT(14)	2515173346260926051	0 2 30 32 96 98 126 128 138 140 150 152 156 158	1792899192324
SPT(16)	2515173404354663029	0 24 54 90 120 124 138 234 274 370 384 388 418 454 484 508	1850992929302
SPT(16)	2515173569615534419	0 12 48 60 64 88 118 154 258 294 324 348 352 364 400 412	2016253800692