Prime p₀= 2570414806735716287 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: fake
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2570413032699542837	0 6 14 24 60 74 80 92 114 126 132 146 182 192 200 206	-1774036173450
STPT(10)	2570413226910640169	0 2 42 44 60 62 78 80 120 122	-1579825076118
STPT(10)	2570413591235225081	0 2 90 92 108 110 126 128 216 218	-1215500491206
SPT(16)	2570414015721637177	0 22 100 120 124 144 184 190 204 210 250 270 274 294 372 394	-791014079110
SPT(16)	2570414165324146621	0 22 42 76 78 132 138 186 232 280 286 340 342 376 396 418	-641411569666
SPT(16)	2570414433351893197	0 4 24 42 90 94 124 132 172 180 210 214 262 280 300 304	-373383823090
STPT(10)	2570414817879450467	0 2 72 74 102 104 132 134 204 206	11143734180
STPT(10)	2570415157679196011	0 2 30 32 60 62 90 92 120 122	350943479724
STPT(12)	2570415489431313569	0 2 12 14 42 44 48 50 78 80 90 92	682695597282
SPT(16)	2570415794041029287	0 56 86 114 132 140 192 222 224 254 306 314 332 360 390 446	987305313000
STPT(10)	2570415947478714089	0 2 18 20 30 32 42 44 60 62	1140742997802