Prime p₀= 4387503732681102893 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 90 14 10 2 34 18 66 56 66 18 34 2 10 14 90 (?)
a_n: 0 90 104 114 116 150 168 234 290 356 374 408 410 420 434 524
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: 524
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 90 14 10 2 34 18 66 56

STPT(10)	4387500978425261777	0 2 90 92 150 152 210 212 300 302	-2754255841116
SPT(16)	4387501228682631863	0 20 30 44 56 90 96 138 146 188 194 228 240 254 264 284	-2503998471030
STPT(10)	4387501900420013729	0 2 48 50 90 92 132 134 180 182	-1832261089164
STPT(10)	4387502862469386761	0 2 6 8 48 50 90 92 96 98	-870211716132
STPT(10)	4387503494646759959	0 2 42 44 90 92 138 140 180 182	-238034342934
SPT(16)	4387503687291773413	0 30 46 54 78 96 154 156 178 180 238 256 280 288 304 334	-45389329480
SPT(16)	4387504089218955751	0 12 16 28 36 40 46 48 70 72 78 82 90 102 106 118	356537852858
STPT(10)	4387504623411344387	0 2 30 32 42 44 54 56 84 86	890730241494
STPT(10)	4387505142996338681	0 2 36 38 108 110 180 182 216 218	1410315235788
SPT(16)	4387505181254518483	0 6 24 28 30 94 144 196 198 250 300 364 366 370 388 394	1448573415590
SPT(16)	4387505489668879033	0 4 24 66 78 100 144 210 334 400 444 466 478 520 540 544	1756987776140