Prime p₀= 2561910312211265537 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: Orange Kid
db: batch=82, k=10, 2 28 2 10 2

SPT(16)	2561909594533220149	0 52 54 60 72 84 130 142 150 162 208 220 232 238 240 292	-717678045388
STPT(10)	2561909660364992261	0 2 30 32 78 80 126 128 156 158	-651846273276
SPT(16)	2561909720188145603	0 6 68 80 104 180 188 194 210 216 224 300 324 336 398 404	-592023119934
TPT(16)	2561909726873833067	0 2 42 44 90 92 174 176 240 242 264 266 270 272 294 296	-585337432470
SPT(16)	2561909810913866177	0 32 36 42 92 102 114 120 206 212 224 234 284 290 294 326	-501297399360
SPT(16)	2561909956648638053	0 8 24 90 96 104 146 170 174 198 240 248 254 320 336 344	-355562627484
STPT(10)	2561910879035972831	0 2 6 8 48 50 90 92 96 98	566824707294
STPT(10)	2561910901392467267	0 2 30 32 42 44 54 56 84 86	589181201730
STPT(10)	2561910911010527309	0 2 48 50 60 62 72 74 120 122	598799261772
TPT(14)	2561911090201364969	0 2 12 14 18 20 42 44 132 134 138 140 168 170	777990099432
STPT(10)	2561911512101591561	0 2 6 8 18 20 30 32 36 38	1199890326024