Minimum coprime number conjecture for GP(3k,k)

Let $k\geq 2$, and let $GP(3k,k)$ be the generalized Petersen graph. Let $\mathfrak{pr}(G)$ denote its minimum coprime number. The $GP(3k,k)$ minimum-coprime-number conjecture.

$$\mathfrak{pr}(GP(3k,k))=\begin{cases}7k & \text{if } k \text{ is odd},\\ 7k+1 & \text{if } k \text{ is even}.\end{cases}$$

The source presents this as a conjecture motivated by independence-number bounds and reports verification only for small cases.