029: Prime queen attacking problem

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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.