Prime p₀= 1571276749729363277 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: crashtech
db: batch=78, k=10, 2 10 2 28 2

SPT(16)	1571275117706765929	0 22 24 34 58 82 84 108 124 148 150 174 198 208 210 232	-1632022597348
STPT(10)	1571275462098679859	0 2 18 20 30 32 42 44 60 62	-1287630683418
STPT(10)	1571275795492553597	0 2 42 44 72 74 102 104 144 146	-954236809680
SPT(20)	1571276017291664429	0 20 42 78 84 180 240 252 258 260 342 344 350 362 422 518 524 560 582 602	-732437698848
SPT(16)	1571276329205917801	0 18 36 42 78 90 108 120 178 190 208 220 256 262 280 298	-420523445476
SPT(16)	1571276541837021191	0 2 6 30 86 98 120 138 170 188 210 222 278 302 306 308	-207892342086
STPT(10)	1571277432739074017	0 2 24 26 42 44 60 62 84 86	683009710740
STPT(10)	1571277485369211671	0 2 6 8 18 20 30 32 36 38	735639848394
STPT(10)	1571277858657367037	0 2 60 62 102 104 144 146 204 206	1108928003760
STPT(10)	1571277936409540361	0 2 30 32 60 62 90 92 120 122	1186680177084
SPT(16)	1571278056624518843	0 68 84 150 216 228 240 324 350 434 446 458 524 590 606 674	1306895155566