Prime p₀= 1253024346142344077 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: Megacruncher
db: batch=77, k=10, 2 28 2 10 2

SPT(16)	1253022945407290033	0 36 54 106 126 184 286 330 334 378 480 538 558 610 628 664	-1400735054044
SPT(16)	1253023004049665869	0 4 52 82 88 94 114 118 234 238 258 264 270 300 348 352	-1342092678208
SPT(16)	1253023042522801139	0 72 84 102 122 168 182 218 234 270 284 330 350 368 380 452	-1303619542938
SPT(16)	1253023104648851603	0 6 8 14 48 68 78 140 174 236 246 266 300 306 308 314	-1241493492474
SPT(16)	1253023250094334801	0 10 36 70 96 166 186 190 276 280 300 370 396 430 456 466	-1096048009276
STPT(10)	1253023303111332407	0 2 54 56 72 74 90 92 144 146	-1043031011670
STPT(10)	1253024645806822151	0 2 6 8 48 50 90 92 96 98	299664478074
SPT(16)	1253024665376417861	0 20 32 48 56 78 92 120 158 186 200 222 230 246 258 278	319234073784
SPT(16)	1253024866124920457	0 44 60 72 74 140 144 150 164 170 174 240 242 254 270 314	519982576380
STPT(10)	1253025163762927019	0 2 48 50 90 92 132 134 180 182	817620582942
STPT(10)	1253025234057390791	0 2 6 8 48 50 90 92 96 98	887915046714