Prime p₀= 2798490797154562577 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: Roadranner
db: batch=82, k=10, 2 10 2 28 2

SPT(18)	2798489727079189463	0 14 36 56 60 78 126 134 138 146 150 158 206 224 228 248 270 284	-1070075373114
STPT(10)	2798489777602771697	0 2 30 32 42 44 54 56 84 86	-1019551790880
SPT(16)	2798489855913253237	0 4 40 64 114 126 130 154 156 180 184 196 246 270 306 310	-941241309340
SPT(16)	2798490315747825779	0 20 38 90 98 108 110 134 168 192 194 204 212 264 282 302	-481406736798
SPT(16)	2798490331522239131	0 30 72 78 92 98 138 140 198 200 240 246 260 266 308 338	-465632323446
STPT(10)	2798490763038407621	0 2 30 32 60 62 90 92 120 122	-34116154956
SPT(16)	2798490815969119049	0 20 42 44 62 74 80 122 150 192 198 210 228 230 252 272	18814556472
SPT(16)	2798490863128441409	0 48 74 84 108 140 152 192 260 300 312 344 368 378 404 452	65973878832
SPT(16)	2798490887391578167	0 6 12 24 66 70 90 136 150 196 216 220 262 274 280 286	90237015590
STPT(10)	2798491312530531557	0 2 30 32 60 62 90 92 120 122	515375968980
STPT(10)	2798491571407812701	0 2 36 38 78 80 120 122 156 158	774253250124