Factorization into two orthogonal quasi-prime matrices

Let $n$ be an even natural number greater than $2$. A quasi-prime matrix is a matrix that is the product of two quasi-invertible semi-prime matrices, where a semi-prime matrix is a rectangular matrix whose smaller dimension is prime. Two $n\times n$ matrices are orthogonal when $AB^{*}=A^{*}B=O$. The orthogonal quasi-prime factorization conjecture. Every $n\times n$ matrix is the sum of two orthogonal quasi-prime matrices.

This conjecture concerns decomposing even-order matrices into structured, mutually orthogonal factors. The supplied context does not state whether it has been resolved.