Prime p₀= 2574627575345378867 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: [SG]ATA-Rolf
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2574625030887568567	0 72 100 102 150 156 174 186 310 322 340 346 394 396 424 496	-2544457810300
STPT(10)	2574625443095363639	0 2 42 44 60 62 78 80 120 122	-2132250015228
SPT(16)	2574626537540779357	0 12 30 42 72 132 142 180 256 294 304 364 394 406 424 436	-1037804599510
SPT(20)	2574627018185198269	0 18 42 144 150 208 222 234 238 264 298 324 328 340 354 412 418 520 544 562	-557160180598
SPT(16)	2574627353489361367	0 16 22 70 124 142 162 172 204 214 234 252 306 354 360 376	-221856017500
SPT(13)	2574627437791236413	0 6 18 48 60 186 258 330 456 468 498 510 516	-137554142454
STPT(10)	2574627863412448841	0 2 6 8 48 50 90 92 96 98	288067069974
SPT(16)	2574627868359465313	0 16 24 28 70 154 184 238 246 300 330 414 456 460 468 484	293014086446
STPT(10)	2574627900946810559	0 2 48 50 90 92 132 134 180 182	325601431692
TPT(14)	2574627946682381411	0 2 48 50 258 260 306 308 546 548 570 572 678 680	371337002544
STPT(10)	2574628403367166841	0 2 36 38 78 80 120 122 156 158	828021787974