Prime p₀= 2068535047323266057 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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=80, k=10, 2 28 2 10 2

STPT(10)	2068534047877436759	0 2 42 44 90 92 138 140 180 182	-999445829298
SPT(16)	2068534093690650059	0 12 62 90 108 110 138 308 312 482 510 512 530 558 608 620	-953632615998
STPT(10)	2068534333823467421	0 2 6 8 18 20 30 32 36 38	-713499798636
STPT(10)	2068534422123024587	0 2 30 32 42 44 54 56 84 86	-625200241470
SPT(16)	2068534625683847147	0 2 32 36 150 164 176 186 260 270 282 296 410 414 444 446	-421639418910
STPT(10)	2068534838317486109	0 2 18 20 30 32 42 44 60 62	-209005779948
SPT(16)	2068535240666124409	0 40 112 130 142 160 168 204 208 244 252 270 282 300 372 412	193342858352
SPT(16)	2068535947960674421	0 12 28 40 78 88 106 132 166 192 210 220 258 270 286 298	900637408364
SPT(16)	2068536261617600081	0 26 60 66 72 110 128 150 158 180 198 236 242 248 282 308	1214294334024
SPT(16)	2068536466805772949	0 10 34 112 124 144 172 214 300 342 370 390 402 480 504 514	1419482506892
SPT(16)	2068536701971457203	0 54 58 84 114 126 150 154 180 184 208 220 250 276 280 334	1654648191146