Sierpiński's conjecture on primes in rows of an n by n matrix

Let $n>1$ be an integer. Arrange the integers $1,2,\ldots,n^2$ in an $n\times n$ matrix, with row $r$ consisting of the integers $(r-1)n+1,\ldots,rn$:

$$\begin{matrix} 1 & 2 & \cdots & n\\ n+1 & n+2 & \cdots & 2n\\ 2n+1 & 2n+2 & \cdots & 3n\\ \cdots & \cdots & \cdots & \cdots\\ (n-1)n+1 & (n-1)n+2 & \cdots & n^2 \end{matrix}$$

Sierpiński's conjecture. Every row of this matrix contains at least one prime number.

This is presented as a beautiful problem and is attributed by the source to Ribenboim; no resolution is given in the paper.