Prime p₀= 2123547137235823589 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 46 2 46 2 40 2 (?)
a_n: 0 2 42 44 90 92 138 140 180 182
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: 182
Found by: Chooka
db: batch=80, k=10, 2 40 2 46 2

SPT(16)	2123546683410918769	0 34 48 78 84 94 120 124 234 238 264 274 280 310 324 358	-453824904820
STPT(10)	2123546772249041351	0 2 36 38 78 80 120 122 156 158	-364986782238
SPT(16)	2123546954294258791	0 6 12 16 22 70 72 96 232 256 258 306 312 316 322 328	-182941564798
SPT(16)	2123546975664135481	0 22 42 66 70 102 232 250 342 360 490 522 526 550 570 592	-161571688108
STPT(10)	2123547085351166351	0 2 30 32 60 62 90 92 120 122	-51884657238
SPT(20)	2123547122124388379	0 2 12 38 72 110 144 150 158 168 224 234 242 248 282 320 354 380 390 392	-15111435210
SPT(16)	2123547177635239669	0 10 18 48 82 84 112 130 132 150 178 180 214 244 252 262	40399416080
STPT(10)	2123547195043456937	0 2 30 32 42 44 54 56 84 86	57807633348
STPT(10)	2123547269047831379	0 2 18 20 30 32 42 44 60 62	131812007790
SPT(16)	2123547427881454543	0 24 66 78 106 196 216 220 234 238 258 348 376 388 430 454	290645630954
STPT(10)	2123547639149512349	0 2 12 14 90 92 168 170 180 182	501913688760