Prime p₀= 2565123531667585697 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 52 2 16 2 16 2 52 2 (?)
a_n: 0 2 54 56 72 74 90 92 144 146
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: 146
Found by: JayPi
db: batch=82, k=10, 2 52 2 16 2

SPT(16)	2565122278867939711	0 6 16 42 46 48 76 130 228 282 310 312 316 342 352 358	-1252799645986
STPT(10)	2565122311381373837	0 2 30 32 60 62 90 92 120 122	-1220286211860
SPT(16)	2565122568338029207	0 6 30 60 82 166 222 226 270 274 330 414 436 466 490 496	-963329556490
SPT(16)	2565122847335972377	0 4 84 102 112 160 220 264 292 336 396 444 454 472 552 556	-684331613320
STPT(10)	2565123168029189627	0 2 30 32 72 74 114 116 144 146	-363638396070
STPT(10)	2565123450329567717	0 2 42 44 72 74 102 104 144 146	-81338017980
TPT(14)	2565123785766759209	0 2 198 200 222 224 312 314 390 392 408 410 432 434	254099173512
SPT(16)	2565124066946519293	0 10 34 88 94 144 174 270 304 400 430 480 486 540 564 574	535278933596
SPT(16)	2565124223391956357	0 24 80 104 132 134 150 182 252 284 300 302 330 354 410 434	691724370660
STPT(10)	2565124532156913227	0 2 54 56 72 74 90 92 144 146	1000489327530
SPT(16)	2565124851109739747	0 2 14 36 54 72 80 86 90 96 104 122 140 162 174 176	1319442154050