Prime p₀= 2564378036637627167 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 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 22 2 16 2

SPT(16)	2564375855727945967	0 4 36 52 70 94 102 120 136 154 162 186 204 220 252 256	-2180909681200
STPT(10)	2564375939098735997	0 2 42 44 72 74 102 104 144 146	-2097538891170
SPT(16)	2564376182468506579	0 42 52 78 90 108 112 148 192 228 232 250 262 288 298 340	-1854169120588
SPT(16)	2564376544586385103	0 40 54 66 94 124 126 130 150 154 156 186 214 226 240 280	-1492051242064
SPT(16)	2564377949561965939	0 12 22 42 48 54 58 78 154 174 178 184 190 210 220 232	-87075661228
SPT(16)	2564378002730004479	0 2 12 14 18 42 44 84 128 168 170 194 198 200 210 212	-33907622688
STPT(10)	2564379280696090157	0 2 24 26 42 44 60 62 84 86	1244058462990
SPT(16)	2564379319366019717	0 14 60 80 90 126 162 174 242 254 290 326 336 356 402 416	1282728392550
SPT(16)	2564379367568485903	0 18 36 60 78 88 108 120 244 256 276 286 304 328 346 364	1330930858736
STPT(12)	2564379480543224567	0 2 12 14 42 44 192 194 222 224 234 236	1443905597400
SPT(16)	2564379934704982091	0 12 20 36 96 98 168 180 218 230 300 302 362 378 386 398	1898067354924