### Magic prime square

Why using sequencial numbers in the magic square? You can also use prime numbers to produce a magic prime square.

3x3 magic prime square (with the smallest possible prime numbers)

 177 177 177 177 177 177 47 113 17 177 29 59 89 177 101 5 71

Source:  Lev Liberant, April 2011

N.B.: Number 1 is officially no prime number. If we allow 1 to be a prime number, we get:

3x3 magic prime square (with the smallest possible prime numbers, including 1)

 111 111 111 111 111 111 67 1 43 111 13 37 61 111 31 73 7

3x3 magic prime square 9 sequencial prime numbers

The real numbers are:

 14800028129 14800028141 14800028153 14800028159 14800028171 14800028183 14800028189 14800028201 14800028213

 513 513 513 513 513 513 159 153 201 513 213 171 129 513 141 189 183

4x4 panmagic prime square

 240 240 240 240 240 240 240 7 107 23 103 240 89 37 73 41 240 240 240 97 17 113 13 240 240 240 47 79 31 83 240 240 240 240 240 240 240 240 240 240 240

Source:  book “De pracht van priemgetallen” by Paul Levrie and Rudi Penne

4x4 symmetric magic prime square

 9500 9500 9500 9500 9500 9500 9500 2837 2087 2687 1889 9500 2753 1823 1223 3701 9500 1049 3527 2927 1997 9500 2861 2063 2663 1913

(4x4 in) 6x6 panmagic prime square

 14250 14250 14250 14250 14250 14250 14250 14250 14250 1361 3491 2393 2333 2963 1709 14250 1811 2837 2087 2687 1889 2939 14250 14250 14250 2819 2753 1823 1223 3701 1931 14250 14250 14250 2879 1049 3527 2927 1997 1871 14250 14250 14250 2339 2861 2063 2663 1913 2411 14250 14250 14250 3041 1259 2357 2417 1787 3389 14250 14250

(4x4 in 6x6 in) 8x8 magic prime square

 19000 19000 19000 19000 19000 19000 19000 19000 19000 19000 19000 2621 2477 2039 1289 3251 1583 3533 2207 19000 3257 1361 3491 2393 2333 2963 1709 1493 19000 2609 1811 2837 2087 2687 1889 2939 2141 19000 2777 2819 2753 1823 1223 3701 1931 1973 19000 2351 2879 1049 3527 2927 1997 1871 2399 19000 1283 2339 2861 2063 2663 1913 2411 3467 19000 1559 3041 1259 2357 2417 1787 3389 3191 19000 2543 2273 2711 3461 1499 3167 1217 2129

Source:  A. W. Johnson, Jr., J. Recreational Mathematics 15:2, 1982-83, p. 84

12x12 prime square of J.N. Muncey with the 144 smallest odd prime numbers (with 1)

 4514 4514 4514 4514 4514 4514 4514 4514 4514 4514 4514 4514 4514 4514 4514 1 823 821 809 811 797 19 29 313 31 23 37 4514 89 83 211 79 641 631 619 709 617 53 43 739 4514 97 227 103 107 193 557 719 727 607 139 757 281 4514 223 653 499 197 109 113 563 479 173 761 587 157 4514 367 379 521 383 241 467 257 263 269 167 601 599 4514 349 359 353 647 389 331 317 311 409 307 293 449 4514 503 523 233 337 547 397 421 17 401 271 431 433 4514 229 491 373 487 461 251 443 463 137 439 457 283 4514 509 199 73 541 347 191 181 569 577 571 163 593 4514 661 101 643 239 691 701 127 131 179 613 277 151 4514 659 673 677 683 71 67 61 47 59 743 733 41 4514 827 3 7 5 13 11 787 769 773 419 149 751

Source:  book “De pracht van priemgetallen” by Paul Levrie and Rudi Penne

4x4 semi bimagic prime square (with smallest possible prime numbers)

 1190 1190 1190 1190 1190 29 293 641 227 1190 277 659 73 181 1190 643 101 337 109 1190 241 137 139 673

 549100 549100 549100 549100 549100 841 85849 410881 51529 549100 76729 434281 5329 32761 549100 413449 10201 113569 11881 549100 58081 18769 19321 452929

Source:  Article of Christian Boyer, The Mathematical Intelligencer, Vol. 27, N. 2, 2005, pages 52-64

Magic prime square A

 1456 1456 1456 1456 1456 1456 1456 67 241 577 571 1456 547 769 127 13 1456 223 139 421 673 1456 619 307 331 199

Magic prime square B

 6544 6544 6544 6544 6544 6544 6544 1933 1759 1423 1429 6544 1453 1231 1873 1987 6544 1777 1861 1579 1327 6544 1381 1693 1669 1801

Magic prime square A + B

 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000

Source:  Designed by John E. Everett (July, 2000)

N.B.: Emily Verbruggen from Belgium send me the prime magic squares from the book "De pracht van priemgetallen".

Specials, Magic prime square.xls