Year and Square

The simplest and in some ways greatest magic square is this:

6 1 8
7 5 3
2 9 4 (Magic total = 15)

All rows and columns sum to 15 and so do both diagonals. Using other sets of numbers, you can create an infinite number of further 3×3 magic squares. Here’s one using only prime numbers and 1:

43 01 67
61 37 13
07 73 31 (Magic=111)

The magic total is 111, which is 3 x 37, just as 15 = 3 x 5. It’s an interesting but untaxing exercise to prove that, for all 3×3 magic squares, the magic total is three times the central number. So you can use only prime numbers in a 3×3 square, but you can’t have a prime number as the magic total (unless you use fractions and so on).

And guess what? 2019 = 3 x 667, the first prime number after 666. So I decided to see if I could find an all-prime magic squares whose magic total was 2019. I found nine of them (and 9 = 3 x 3).

1117 0019 0883
0439 0673 0907
0463 1327 0229 (Magic=2019)

1069 0067 0883
0487 0673 0859
0463 1279 0277 (Magic=2019)

1063 0229 0727
0337 0673 1009
0619 1117 0283 (Magic=2019)

0883 0313 0823
0613 0673 0733
0523 1033 0463 (Magic=2019)

0619 0337 1063
1117 0673 0229
0283 1009 0727 (Magic=2019)

0463 0439 1117
1327 0673 0019
0229 0907 0883 (Magic=2019)

0463 0487 1069
1279 0673 0067
0277 0859 0883 (Magic=2019)

0379 0607 1033
1327 0673 0019
0313 0739 0967 (Magic=2019)

0523 0613 0883
1033 0673 0313
0463 0733 0823 (Magic=2019)