
In the 1992 I see this prime magic square in the number 114 of McMicrocomputer magazine. How you can see the square is of order 12, and the inserted numbers are all primes:
1 823 821 809 811 797 19 29 313 31 23 37 89 83 211 79 641 631 619 709 617 53 43 739 97 227 103 107 193 557 719 727 607 139 757 281 223 653 499 197 109 113 563 479 173 761 587 157 367 379 521 383 241 467 257 263 269 167 601 599 349 359 353 647 389 331 317 311 409 307 293 449 503 523 233 337 547 397 421 17 401 271 431 433 229 491 373 487 461 251 443 463 137 439 457 283 509 199 73 541 347 191 181 569 577 571 163 593 661 101 643 239 691 701 127 131 179 613 277 151 659 673 677 683 71 67 61 47 59 743 733 41 827 3 7 5 13 11 787 769 773 419 149 751In detail, the numbers are the first N*N primes, where the prime 2 is substitute with 1 (because if we use an even number, we can not obtain the magic constant), and the magic constant is equal to 4514.
The above square was created by J. N. Muncey in 1913!
Murcey also demonstrate that the order 12 is the smallest order for this type of
magic square.
Well, there is of that stay awake the night (because he founds those results when a computer don't exist)!
After saw this square, I wanted to study this category of magic squares, but I
had little time for research, so the first results have been had only in late
1996, and the final result is today not reached.
I don't know if other people have study this squares, so if the algorithms
that I have build are similar (or the same) that eventually other people,
the only thing that I could tell is that the world is small.
Remember that you can download all the programs that I have use
(sources).
Magic Square  Tognon Stefano Research 