Prime p₀= 2353811230217886557 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: MarkRBright
db: batch=81, k=10, 2 22 2 16 2

SPT(16)	2353809162660464059	0 22 24 42 88 94 102 160 162 220 228 234 280 298 300 322	-2067557422498
SPT(16)	2353809391870017713	0 48 90 98 120 140 146 158 216 228 234 254 276 284 326 374	-1838347868844
SPT(16)	2353810539709748891	0 30 36 38 72 80 90 128 210 248 258 266 300 302 308 338	-690508137666
STPT(10)	2353810742724507509	0 2 42 44 60 62 78 80 120 122	-487493379048
TPT(14)	2353810934358525779	0 2 18 20 42 44 102 104 168 170 222 224 228 230	-295859360778
SPT(18)	2353810989656935279	0 4 42 60 64 70 72 100 102 130 132 160 162 168 172 190 228 232	-240560951278
SPT(16)	2353811531334092611	0 28 36 40 48 112 138 172 246 280 306 370 378 382 390 418	301116206054
STPT(10)	2353812384599844347	0 2 54 56 132 134 210 212 264 266	1154381957790
SPT(16)	2353812427774576231	0 12 22 66 138 166 190 280 288 378 402 430 502 546 556 568	1197556689674
SPT(16)	2353812428783176463	0 36 56 86 90 170 174 180 254 260 264 344 348 378 398 434	1198565289906
SPT(16)	2353813085054601557	0 32 66 80 84 90 102 116 150 164 176 182 186 200 234 266	1854836715000