Prime p₀= 2453874867025928123 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 44 12 4 24 66 68 6 166 6 68 66 24 4 12 44 (?)
a_n: 0 44 56 60 84 150 218 224 390 396 464 530 554 558 570 614
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: 614
Found by: JayPi
db: batch=82, k=16, 44 12 4 24 66 68 6 166

SPT(16)	2453874094025848579	0 4 54 70 94 108 150 154 204 208 250 264 288 304 354 358	-773000079544
STPT(10)	2453874188619016127	0 2 30 32 42 44 54 56 84 86	-678406911996
STPT(12)	2453874321804906281	0 2 78 80 138 140 150 152 210 212 288 290	-545221021842
STPT(10)	2453874327996113717	0 2 30 32 60 62 90 92 120 122	-539029814406
STPT(10)	2453874662962991909	0 2 12 14 90 92 168 170 180 182	-204062936214
STPT(10)	2453874678389283179	0 2 18 20 30 32 42 44 60 62	-188636644944
SPT(16)	2453874870941092471	0 22 42 60 78 90 228 250 300 322 460 472 490 508 528 550	3915164348
SPT(16)	2453874896441587063	0 30 64 106 154 156 196 210 274 288 328 330 378 420 454 484	29415658940
SPT(16)	2453875132413690707	0 30 36 96 122 152 186 192 254 260 294 324 350 410 416 446	265387762584
SPT(16)	2453875829894755451	0 20 38 66 72 98 230 240 248 258 390 416 422 450 468 488	962868827328
TPT(14)	2453875875965522891	0 2 78 80 126 128 150 152 156 158 306 308 366 368	1008939594768