CL-MO 2022

Let $ABC$ be a triangle such that $\angle CAB = 60^o$ . Consider $D, E$ points on sides $AC$ and $AB$ respectively such that $BD$ bisects angle $\angle ABC$ , $CE$ bisects angle $\angle BCA$ and let $I$ be the intersection of them. Prove that $|ID| =|IE|$ .

The $19$ numbers $472$ , $473$ , $...$ , $490$ are juxtaposed in some order to form a $57$ -digit number. Can any of the numbers thus obtained be prime?