The conjecture that almost all three-factor Carmichael numbers are primary

For $x>0$, let $C_3(x)$ denote the number of three-factor Carmichael numbers at most $x$, and let $C'_3(x)$ denote the number of primary three-factor Carmichael numbers at most $x$. Primary Carmichael density conjecture. We have

$$\lim_{x\to\infty}\frac{C'_3(x)}{C_3(x)}=1.$$

The conjecture is motivated by computations and by applying Dickson's conjecture to the universal forms $U_{\mathbf r}(t)$; it predicts that primary Carmichael numbers comprise asymptotically all three-factor Carmichael numbers, and remains open.