Prime p₀= 2678577326731437797 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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: JayPi
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2678575441715935793	0 6 14 36 44 48 80 84 170 174 206 210 218 240 248 254	-1885015502004
STPT(10)	2678575806435000671	0 2 36 38 108 110 180 182 216 218	-1520296437126
SPT(16)	2678575902520618939	0 4 12 42 90 114 142 144 208 210 238 262 310 340 348 352	-1424210818858
SPT(16)	2678575986660335959	0 30 58 64 148 162 184 222 280 318 340 354 438 444 472 502	-1340071101838
SPT(16)	2678576088902886439	0 10 22 72 124 130 142 154 180 192 204 210 262 312 324 334	-1237828551358
STPT(10)	2678577048848592779	0 2 18 20 30 32 42 44 60 62	-277882845018
SPT(16)	2678577487474198561	0 6 10 16 30 40 72 82 186 196 228 238 252 258 262 268	160742760764
SPT(16)	2678577609172741831	0 66 88 100 102 126 130 142 156 168 172 196 198 210 232 298	282441304034
TPT(14)	2678577710159703017	0 2 30 32 42 44 54 56 162 164 180 182 222 224	383428265220
SPT(16)	2678577974151473543	0 8 78 114 120 144 146 156 188 198 200 224 230 266 336 344	647420035746
STPT(10)	2678578052349924479	0 2 18 20 30 32 42 44 60 62	725618486682