Prime p₀= 2356556766790706717 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: Landjunge
db: batch=81, k=10, 2 10 2 28 2

STPT(10)	2356555693952716379	0 2 12 14 90 92 168 170 180 182	-1072837990338
STPT(10)	2356555817893785689	0 2 18 20 30 32 42 44 60 62	-948896921028
STPT(10)	2356555865584920029	0 2 18 20 30 32 42 44 60 62	-901205786688
SPT(16)	2356556243385700579	0 12 48 60 72 82 90 132 220 262 270 280 292 304 340 352	-523405006138
SPT(16)	2356556568362568287	0 66 92 102 122 156 192 266 270 344 380 414 434 444 470 536	-198428138430
STPT(10)	2356556720303520737	0 2 30 32 72 74 114 116 144 146	-46487185980
STPT(10)	2356557265969164161	0 2 36 38 78 80 120 122 156 158	499178457444
SPT(16)	2356557281944512169	0 40 64 130 154 160 172 178 204 210 222 228 252 318 342 382	515153805452
STPT(10)	2356557369374347169	0 2 18 20 30 32 42 44 60 62	602583640452
STPT(10)	2356557847209983741	0 2 30 32 78 80 126 128 156 158	1080419277024
SPT(16)	2356557983806673629	0 42 54 154 168 184 208 220 222 234 258 274 288 388 400 442	1217015966912