Prime p₀= 4387505489668879033 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 4 20 42 12 22 44 66 124 66 44 22 12 42 20 4 (?)
a_n: 0 4 24 66 78 100 144 210 334 400 444 466 478 520 540 544
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: 544
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 4 20 42 12 22 44 66 124

SPT(16)	4387503687291773413	0 30 46 54 78 96 154 156 178 180 238 256 280 288 304 334	-1802377105620
SPT(16)	4387503732681102893	0 90 104 114 116 150 168 234 290 356 374 408 410 420 434 524	-1756987776140
SPT(16)	4387504089218955751	0 12 16 28 36 40 46 48 70 72 78 82 90 102 106 118	-1400449923282
STPT(10)	4387504623411344387	0 2 30 32 42 44 54 56 84 86	-866257534646
STPT(10)	4387505142996338681	0 2 36 38 108 110 180 182 216 218	-346672540352
SPT(16)	4387505181254518483	0 6 24 28 30 94 144 196 198 250 300 364 366 370 388 394	-308414360550
STPT(10)	4387505603711992427	0 2 30 32 42 44 54 56 84 86	114043113394
SPT(16)	4387506056570532473	0 54 68 138 158 198 224 230 264 270 296 336 356 426 440 494	566901653440
TPT(14)	4387506103514095337	0 2 12 14 114 116 180 182 240 242 282 284 360 362	613845216304
STPT(10)	4387506601209346187	0 2 24 26 42 44 60 62 84 86	1111540467154
STPT(10)	4387506635708325329	0 2 12 14 90 92 168 170 180 182	1146039446296