In [1] the following problem is described:

- The chessboard shown above has \(8\times 8 = 64\) cells.
- Place numbers 1 through 64 in the cells such that the next number is either directly left, right, below, or above the current number.
- The dark cells must be occupied by prime numbers. Note there are 18 dark cells, and 18 primes in the sequence \(1,\dots,64\). These prime numbers are: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61.

This problem looks very much like the Numbrix puzzle [3]. We don't have the **given **cells that are provided in Numbrix, but instead, we have some cells that need to be covered by prime numbers.

The path formed by the consecutive values looks like how a rook moves on a chessboard. Which explains the title of this post (and of the original post). If we require a **proper tour** we need values 1 and 64 to be neighbors. Otherwise, if this is not required, I think a better term is: **Hamiltonian path**. I'll discuss both cases, starting with the Hamiltonian path problem.