Prime p₀= 4387506635708325329 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 76 2 76 2 10 2 (?)
a_n: 0 2 12 14 90 92 168 170 180 182
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: 182
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 10 2 76 2

SPT(16)	4387505181254518483	0 6 24 28 30 94 144 196 198 250 300 364 366 370 388 394	-1454453806846
SPT(16)	4387505489668879033	0 4 24 66 78 100 144 210 334 400 444 466 478 520 540 544	-1146039446296
STPT(10)	4387505603711992427	0 2 30 32 42 44 54 56 84 86	-1031996332902
SPT(16)	4387506056570532473	0 54 68 138 158 198 224 230 264 270 296 336 356 426 440 494	-579137792856
TPT(14)	4387506103514095337	0 2 12 14 114 116 180 182 240 242 282 284 360 362	-532194229992
STPT(10)	4387506601209346187	0 2 24 26 42 44 60 62 84 86	-34498979142
SPT(16)	4387506724870977677	0 6 162 180 204 254 266 270 296 300 312 362 386 404 560 566	89162652348
STPT(10)	4387508038089069077	0 2 30 32 60 62 90 92 120 122	1402380743748
SPT(16)	4387508070418468783	0 16 28 90 154 184 190 204 250 264 270 300 364 426 438 454	1434710143454
STPT(10)	4387509577207924511	0 2 36 38 78 80 120 122 156 158	2941499599182
SPT(16)	4387509771591967913	0 36 78 84 120 126 138 156 158 176 188 194 230 236 278 314	3135883642584