Prime p₀= 2166210890693135981 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 28 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 90 92 120 122
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: 122
Found by: ginga
db: batch=81, k=10, 2 28 2 28 2

SPT(16)	2166208624157364233	0 38 44 54 90 126 168 186 278 296 338 374 410 420 426 464	-2266535771748
STPT(10)	2166208780144506239	0 2 18 20 30 32 42 44 60 62	-2110548629742
SPT(16)	2166209261833757969	0 50 90 132 134 192 204 234 320 350 362 420 422 464 504 554	-1628859378012
SPT(16)	2166209669918121077	0 12 20 32 66 84 96 104 222 230 242 260 294 306 314 326	-1220775014904
STPT(10)	2166209884801380947	0 2 12 14 42 44 72 74 84 86	-1005891755034
STPT(10)	2166210218163723461	0 2 36 38 78 80 120 122 156 158	-672529412520
SPT(16)	2166211215687829381	0 18 58 168 190 208 238 250 396 408 438 456 478 588 628 646	324994693400
STPT(10)	2166211775907002567	0 2 42 44 72 74 102 104 144 146	885213866586
SPT(16)	2166211999186249451	0 2 50 78 86 110 120 138 290 308 318 342 350 378 426 428	1108493113470
TPT(14)	2166212204304945359	0 2 12 14 78 80 120 122 132 134 138 140 210 212	1313611809378
SPT(16)	2166212312959322609	0 14 72 104 182 288 324 372 380 428 464 570 648 680 738 752	1422266186628