Prime p₀= 4310396137944112421 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: Chooka
db: batch=85, k=10, 2 4 2 10 2

SPT(16)	4310393809886803069	0 22 28 138 160 172 222 250 252 280 330 342 364 474 480 502	-2328057309352
STPT(10)	4310394382836566417	0 2 30 32 42 44 54 56 84 86	-1755107546004
SPT(16)	4310394939328229491	0 36 76 108 148 150 160 168 328 336 346 348 388 420 460 496	-1198615882930
TPT(16)	4310395368781364789	0 2 78 80 120 122 168 170 210 212 252 254 300 302 342 344	-769162747632
STPT(14)	4310395368781364867	0 2 42 44 90 92 132 134 174 176 222 224 264 266	-769162747554
STPT(10)	4310395682596380197	0 2 60 62 72 74 84 86 144 146	-455347732224
STPT(10)	4310396377223820197	0 2 30 32 72 74 114 116 144 146	239279707776
SPT(16)	4310396424086481119	0 2 14 24 68 84 132 152 210 230 278 294 338 348 360 362	286142368698
STPT(10)	4310396519607009509	0 2 18 20 30 32 42 44 60 62	381662897088
SPT(16)	4310397102473074693	0 28 34 36 100 108 114 126 148 160 166 174 238 240 246 274	964528962272
STPT(10)	4310397216644728421	0 2 36 38 78 80 120 122 156 158	1078700616000