Prime p₀= 2423999314068347593 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 6 52 18 68 54 6 4 38 4 6 54 68 18 52 6 (?)
a_n: 0 6 58 76 144 198 204 208 246 250 256 310 378 396 448 454
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 454
Found by: Roadranner
db: batch=82, k=16, 6 52 18 68 54 6 4 38

SPT(16)	2423997572175264191	0 2 8 42 78 86 110 122 156 168 192 200 236 270 276 278	-1741893083402
SPT(13)	2423997634964719789	0 30 72 108 120 162 180 198 240 252 288 330 360	-1679103627804
SPT(16)	2423997925585226521	0 12 48 126 136 142 160 220 258 318 336 342 352 430 466 478	-1388483121072
SPT(16)	2423998655023686259	0 10 72 82 138 150 168 208 264 304 322 334 390 400 462 472	-659044661334
SPT(16)	2423998954409051611	0 16 42 48 102 126 130 132 196 198 202 226 280 286 312 328	-359659295982
STPT(10)	2423998961219093507	0 2 12 14 42 44 72 74 84 86	-352849254086
SPT(16)	2423999537298840881	0 32 50 98 122 168 230 260 300 330 392 438 462 510 528 560	223230493288
SPT(16)	2423999578112228927	0 42 54 62 72 114 152 266 270 384 422 464 474 482 494 536	264043881334
STPT(10)	2423999869229392841	0 2 30 32 78 80 126 128 156 158	555161045248
SPT(16)	2423999995445818781	0 6 56 78 92 110 120 138 140 158 168 186 200 222 272 278	681377471188
TPT(14)	2424000105865455251	0 2 30 32 78 80 96 98 120 122 180 182 246 248	791797107658