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

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