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.

Bibliography

1

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