# 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 donâ€™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

$$\left[\begin{array}{ccc}\hfill 67\hfill & \hfill 1\hfill & \hfill 43\hfill \\ \hfill 13\hfill & \hfill 37\hfill & \hfill 61\hfill \\ \hfill 31\hfill & \hfill 73\hfill & \hfill 7\hfill \end{array}\right]$$ |

first published by Henry Ernest Dudeney in 1917.

Rudolf Ondrejka constructed this magic square using only Chen primes^{}:

$$\left[\begin{array}{ccc}\hfill 17\hfill & \hfill 89\hfill & \hfill 71\hfill \\ \hfill 113\hfill & \hfill 59\hfill & \hfill 5\hfill \\ \hfill 47\hfill & \hfill 29\hfill & \hfill 101\hfill \end{array}\right]$$ |

The magic constant is 177.

## References

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

Title | prime magic square |
---|---|

Canonical name | PrimeMagicSquare |

Date of creation | 2013-03-22 16:43:28 |

Last modified on | 2013-03-22 16:43:28 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |