029: Prime queen attacking problem

For $n <= 4$, there are no solutions satisfying the constraints of type (1) and type (2).
For $5 <= n <= 8$, optimal solutions are known without any free primes.
Recently, Jacques Tramu has found optimal solutions for $9 <= n <= 10$.
For$ n >= 11$, no optimal solution (i.e. without free primes) exists.