Bubboloni–Praeger–Spiga conjecture for the normal covering number of alternating groups

Let $n=p_1^{\alpha_1}\cdots p_r^{\alpha_r}$, where $r\geq2$, the $p_i$ are primes, $\alpha_i\in\mathbb{N}$, and $p_i<p_j$ for $i<j$. Define

$$g(n):=\frac{n}{2}\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)+2.$$

Assume that $n$ is even, $r\geq2$, and $n\neq2p_2,12$.

Normal covering conjecture for $A_n$.

$$\gamma(A_n)=g(n).$$

This is the alternating-group counterpart of the proposed formula for $\gamma(S_n)$. The paper establishes linear growth and discusses evidence for the formula, but the exact value remains open in the stated generality.