Prime p₀= 2114376916145019731 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: gemini8
db: batch=80, k=10, 2 4 2 10 2

SPT(16)	2114375280748161259	0 58 82 118 142 148 184 220 222 258 294 300 324 360 384 442	-1635396858472
STPT(10)	2114375716853115887	0 2 54 56 132 134 210 212 264 266	-1199291903844
SPT(18)	2114375950794044083	0 24 28 66 76 90 138 156 174 220 238 256 304 318 328 366 370 394	-965350975648
SPT(16)	2114376317771672629	0 12 58 108 120 220 280 310 330 360 420 520 532 582 628 640	-598373347102
SPT(16)	2114376390457682537	0 50 54 60 72 92 132 140 216 224 264 284 296 302 306 356	-525687337194
SPT(16)	2114376674931407069	0 32 50 102 110 140 162 228 242 308 330 360 368 420 438 470	-241213612662
SPT(16)	2114377292672908363	0 28 46 174 190 198 216 228 256 268 286 294 310 438 456 484	376527888632
STPT(10)	2114377352964431909	0 2 12 14 90 92 168 170 180 182	436819412178
SPT(20)	2114377431350337331	0 22 28 90 100 150 156 166 168 178 180 190 192 202 208 258 268 330 336 358	515205317600
STPT(10)	2114377625348327387	0 2 42 44 72 74 102 104 144 146	709203307656
TPT(14)	2114377721451702059	0 2 78 80 210 212 372 374 432 434 498 500 510 512	805306682328