Koblitz's prime-order conjecture for CM elliptic curves

Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$. For primes $p$ that split in $K$ and do not divide the conductor of $E$, define

$$d_E=\gcd\left\{\lvert E(\mathbb{F}_p)\rvert\;\middle|\;p\text{ splits in }K,\ p\nmid N_E\right\}.$$

Koblitz's conjecture. There exists a constant $C>0$ such that

$$\#\left\{p\leq x\,\middle|\,p\text{ splits in }K,\ \frac{\lvert E(\mathbb{F}_p)\rvert}{d_E}\text{ is prime}\right\}\sim C\frac{x}{(\log x)^2}.$$

This is a CM version of Koblitz's conjecture, with the fixed common divisor $d_E$ removed from the elliptic-curve group orders. The source provides no resolution status for this assertion.