Prime p₀= 2356309999444795787 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: [SG-2W]Kurzer
db: batch=81, k=10, 2 28 2 10 2

SPT(16)	2356308447717504347	0 44 84 110 116 174 194 200 420 426 446 504 510 536 576 620	-1551727291440
STPT(10)	2356308468581545727	0 2 12 14 72 74 132 134 144 146	-1530863250060
TPT(14)	2356308531668855381	0 2 60 62 120 122 126 128 156 158 210 212 228 230	-1467775940406
SPT(16)	2356309414135502801	0 6 50 72 98 120 132 150 188 206 218 240 266 288 332 338	-585309292986
STPT(10)	2356309568440128359	0 2 42 44 60 62 78 80 120 122	-431004667428
SPT(16)	2356309582991761841	0 12 36 56 78 90 132 140 168 176 218 230 252 272 296 308	-416453033946
SPT(16)	2356310040809080933	0 16 24 76 78 96 100 126 148 174 178 196 198 250 258 274	41364285146
SPT(18)	2356310407475311409	0 38 48 90 140 194 204 222 234 248 260 278 288 342 392 434 444 482	408030515622
STPT(10)	2356310505160349987	0 2 60 62 72 74 84 86 144 146	505715554200
TPT(14)	2356310589364723697	0 2 114 116 144 146 180 182 210 212 234 236 264 266	589919927910
STPT(10)	2356310985143979299	0 2 18 20 60 62 102 104 120 122	985699183512