Prime p₀= 4588263992198457677 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: Stony666
db: batch=85, k=10, 2 28 2 10 2

SPT(16)	4588261903927662559	0 4 34 60 70 78 84 100 132 148 154 162 172 198 228 232	-2088270795118
SPT(16)	4588262131625423327	0 30 114 126 150 152 194 212 264 282 324 326 350 362 446 476	-1860573034350
STPT(12)	4588262294781025697	0 2 42 44 72 74 102 104 132 134 174 176	-1697417431980
STPT(10)	4588262768818886231	0 2 6 8 48 50 90 92 96 98	-1223379571446
SPT(16)	4588263199735342363	0 10 36 46 70 78 108 126 130 148 178 186 210 220 246 256	-792463115314
STPT(10)	4588263771929472137	0 2 24 26 42 44 60 62 84 86	-220268985540
STPT(12)	4588264367674662527	0 2 12 14 30 32 54 56 72 74 84 86	375476204850
STPT(10)	4588264460103837827	0 2 30 32 42 44 54 56 84 86	467905380150
SPT(16)	4588264555890042581	0 8 12 50 60 78 80 102 116 138 140 158 168 206 210 218	563691584904
SPT(16)	4588265014273238443	0 28 144 148 150 190 204 208 216 220 234 274 276 280 396 424	1022074780766
STPT(10)	4588265127810004007	0 2 90 92 132 134 174 176 264 266	1135611546330