Proposed by Christian Bessiere

This problem, posed first by G.L. Honaker, is to put a queen and the $n^2$ numbers $1,…,n^2$, on a $n \times n$ chessboard so that:

1. no two numbers are on the same cell,
2. any number $i+1$ is reachable by a knight move from the cell containing $i$,
3. the number of “free” primes (i.e., primes not attacked by the queen) is minimal.

Note that 1 is not prime, and that the queen does not attack its own cell.

## An Example of solution

A 6x6 chessboard without free primes (the queen is on the cell containing 33):

9 32 3 28 11 30
4 27 10 31 34 1
17 8 33 2 29 12
26 5 16 19 22 35
15 18 7 24 13 20
6 25 14 21 36 23