Primality conjecture for almost every 3-IET

A 3-IET is an interval exchange transformation of an interval cut into three exchanged subintervals, and a measure-preserving system is prime when it has no nontrivial factors.

3-IET primality conjecture. Almost every $3$-IET is prime.

This is given as a specific family-level form of the preceding conjecture. The source contrasts it with the known fact that almost every $3$-IET has self-joinings forming a Paulsen simplex, while the asserted primality remains open.