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prime magic square

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A {\em prime magic square} is a magic square consisting only of prime numbers (the magic constant may be a composite number, especially if the sides are of even length). The primes don't have to be consecutive, though it is sometimes convenient to consider 1 a prime number for the purpose of constructing these squares.

The smallest prime magic square with the smallest possible magic constant (111) is 

$$\begin{bmatrix}
67 & 1 & 43 \\
13 & 37 & 61 \\
31 & 73 & 7 \\
\end{bmatrix}$$

first published by Henry Ernest Dudeney in 1917.

Rudolf Ondrejka constructed this magic square using only Chen primes:

$$\begin{bmatrix}
17 & 89 & 71 \\
113 & 59 & 5 \\
47 & 29 & 101 \\
\end{bmatrix}$$

The magic constant is 177.

\begin{thebibliography}{1}
\bibitem{ed} Dudeney, E. {\it Amusements in Mathematics} New York: Dover (1970): Problem 408
\end{thebibliography}
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