Prime p₀= 2568589632709735301 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: [SG-FC] hl
db: batch=82, k=10, 2 4 2 10 2

SPT(16)	2568588423405675409	0 22 40 88 90 204 208 244 258 294 298 412 414 462 480 502	-1209304059892
STPT(12)	2568588474816445931	0 2 48 50 78 80 90 92 120 122 168 170	-1157893289370
SPT(16)	2568588538893765319	0 12 42 88 130 150 210 220 222 232 292 312 354 400 430 442	-1093815969982
SPT(16)	2568589218882610589	0 24 68 128 152 182 240 248 354 362 420 450 474 534 578 602	-413827124712
SPT(16)	2568589564336167781	0 118 148 166 178 180 198 222 346 370 388 390 402 420 450 568	-68373567520
STPT(12)	2568589568369860577	0 2 24 26 84 86 90 92 150 152 174 176	-64339874724
STPT(10)	2568589666226557637	0 2 42 44 72 74 102 104 144 146	33516822336
SPT(16)	2568589682031831371	0 18 30 60 86 132 138 156 242 260 266 312 338 368 380 398	49322096070
SPT(16)	2568590374578683089	0 22 84 90 108 112 172 214 318 360 420 424 442 448 510 532	741868947788
SPT(16)	2568590552021289823	0 16 24 48 54 70 96 118 216 238 264 280 286 310 318 334	919311554522
SPT(16)	2568590660926664903	0 6 48 74 104 126 144 188 216 260 278 300 330 356 398 404	1028216929602