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# prime magic square

A 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.

# References

- 1 Dudeney, E. Amusements in Mathematics New York: Dover (1970): Problem 408

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## Mathematics Subject Classification

11A41*no label found*

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