Prime p₀= 2306578124905464647 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: FritzB
db: batch=81, k=10, 2 10 2 28 2

SPT(16)	2306577492063726367	0 12 52 70 82 84 120 142 162 184 220 222 234 252 292 304	-632841738280
STPT(10)	2306577496243325489	0 2 18 20 30 32 42 44 60 62	-628662139158
STPT(10)	2306577539635168571	0 2 30 32 78 80 126 128 156 158	-585270296076
STPT(10)	2306577713707648487	0 2 30 32 42 44 54 56 84 86	-411197816160
SPT(16)	2306577983296191811	0 30 42 52 72 100 150 166 192 208 258 286 306 316 328 358	-141609272836
STPT(10)	2306578094695633607	0 2 30 32 60 62 90 92 120 122	-30209831040
SPT(16)	2306578264150853339	0 20 50 62 84 140 164 170 174 180 204 260 282 294 324 344	139245388692
SPT(16)	2306578807696952939	0 2 42 44 98 120 134 138 164 168 182 204 258 260 300 302	682791488292
SPT(16)	2306578839749142199	0 24 30 48 72 94 114 132 220 238 258 280 304 322 328 352	714843677552
TPT(14)	2306578847205825251	0 2 36 38 66 68 78 80 120 122 138 140 180 182	722300360604
SPT(16)	2306579023486415929	0 40 60 88 114 118 154 172 180 198 234 238 264 292 312 352	898580951282