Prime p₀= 2068586431034299019 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
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: 62
Found by: Cruncher Pete
db: batch=80, k=10, 2 16 2 10 2

SPT(16)	2068584672084641939	0 42 138 140 152 224 228 284 348 404 408 480 492 494 590 632	-1758949657080
STPT(10)	2068585079247693197	0 2 42 44 72 74 102 104 144 146	-1351786605822
STPT(10)	2068585353117156659	0 2 42 44 120 122 198 200 240 242	-1077917142360
STPT(10)	2068585584021231731	0 2 30 32 78 80 126 128 156 158	-847013067288
STPT(10)	2068586048614217477	0 2 42 44 72 74 102 104 144 146	-382420081542
STPT(10)	2068586092586689589	0 2 42 44 90 92 138 140 180 182	-338447609430
STPT(10)	2068587010177117277	0 2 12 14 42 44 72 74 84 86	579142818258
STPT(10)	2068587207119008781	0 2 6 8 18 20 30 32 36 38	776084709762
SPT(16)	2068587286302864227	0 24 60 66 90 102 120 132 134 146 164 176 200 206 242 266	855268565208
STPT(10)	2068587606062379299	0 2 78 80 120 122 162 164 240 242	1175028080280
SPT(16)	2068587851132255207	0 24 42 62 104 164 170 182 222 234 240 300 342 362 380 404	1420097956188