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)
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177 |
177 |
177 |
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177 |
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177 |
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177 |
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47 |
113 |
17 |
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177 |
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29 |
59 |
89 |
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177 |
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101 |
5 |
71 |
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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
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14250 |
14250 |
14250 |
14250 |
14250 |
14250 |
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14250 |
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14250 |
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14250 |
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1361 |
3491 |
2393 |
2333 |
2963 |
1709 |
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14250 |
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1811 |
2837 |
2087 |
2687 |
1889 |
2939 |
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14250 |
14250 |
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14250 |
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2819 |
2753 |
1823 |
1223 |
3701 |
1931 |
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14250 |
14250 |
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14250 |
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2879 |
1049 |
3527 |
2927 |
1997 |
1871 |
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14250 |
14250 |
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14250 |
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2339 |
2861 |
2063 |
2663 |
1913 |
2411 |
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14250 |
14250 |
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14250 |
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3041 |
1259 |
2357 |
2417 |
1787 |
3389 |
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14250 |
14250 |
(4x4 in 6x6 in) 8x8 magic prime square
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19000 |
19000 |
19000 |
19000 |
19000 |
19000 |
19000 |
19000 |
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19000 |
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19000 |
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19000 |
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2621 |
2477 |
2039 |
1289 |
3251 |
1583 |
3533 |
2207 |
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19000 |
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3257 |
1361 |
3491 |
2393 |
2333 |
2963 |
1709 |
1493 |
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19000 |
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2609 |
1811 |
2837 |
2087 |
2687 |
1889 |
2939 |
2141 |
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19000 |
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2777 |
2819 |
2753 |
1823 |
1223 |
3701 |
1931 |
1973 |
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19000 |
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2351 |
2879 |
1049 |
3527 |
2927 |
1997 |
1871 |
2399 |
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19000 |
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1283 |
2339 |
2861 |
2063 |
2663 |
1913 |
2411 |
3467 |
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19000 |
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1559 |
3041 |
1259 |
2357 |
2417 |
1787 |
3389 |
3191 |
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19000 |
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2543 |
2273 |
2711 |
3461 |
1499 |
3167 |
1217 |
2129 |
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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)
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1190 |
1190 |
1190 |
1190 |
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1190 |
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29 |
293 |
641 |
227 |
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1190 |
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277 |
659 |
73 |
181 |
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1190 |
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643 |
101 |
337 |
109 |
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1190 |
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241 |
137 |
139 |
673 |
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549100 |
549100 |
549100 |
549100 |
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549100 |
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841 |
85849 |
410881 |
51529 |
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549100 |
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76729 |
434281 |
5329 |
32761 |
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549100 |
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413449 |
10201 |
113569 |
11881 |
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549100 |
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58081 |
18769 |
19321 |
452929 |
Source: Article of Christian Boyer, The Mathematical Intelligencer, Vol. 27, N. 2, 2005, pages 52-64
Magic prime square A
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1456 |
1456 |
1456 |
1456 |
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1456 |
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1456 |
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1456 |
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67 |
241 |
577 |
571 |
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1456 |
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547 |
769 |
127 |
13 |
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1456 |
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223 |
139 |
421 |
673 |
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1456 |
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619 |
307 |
331 |
199 |
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Magic prime square B
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6544 |
6544 |
6544 |
6544 |
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6544 |
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6544 |
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6544 |
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1933 |
1759 |
1423 |
1429 |
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6544 |
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1453 |
1231 |
1873 |
1987 |
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6544 |
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1777 |
1861 |
1579 |
1327 |
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6544 |
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1381 |
1693 |
1669 |
1801 |
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Magic prime square A + B
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2000 |
2000 |
2000 |
2000 |
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2000 |
2000 |
2000 |
2000 |
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2000 |
2000 |
2000 |
2000 |
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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".
