Office Applications and Entertaiment, Magic Squares

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Construction of Prime Number Magic Squares:

André Gérardin, Magic Square (4 x 4)


A1, MC = 52
3 5 7 37
37 7 5 3
5 3 37 7
7 37 3 5
B1, MC = 120
2 8 52 58
52 58 2 8
58 52 8 2
8 2 58 52
A2, MC = 1452
9 25 49 1369
1369 49 25 9
25 9 1369 49
49 1369 9 25
B2, MC = 6136
4 64 2704 3364
2704 3364 4 64
3364 2704 64 4
64 4 3364 2704
C2, MC = 7588
13 89 2753 4733
4073 3413 29 73
3389 2713 1433 53
113 1373 3373 2729


Pan Magic Square (5 x 5)

A1, MC = 194
4 6 16 74 94
16 74 94 4 6
94 4 6 16 74
6 16 74 94 4
74 94 4 6 16
B1, MC = 151
1 5 25 29 91
29 91 1 5 25
5 25 29 91 1
91 1 5 25 29
25 29 91 1 5
A2, MC = 14620
16 36 256 5476 8836
256 5476 8836 16 36
8836 16 36 256 5476
36 256 5476 8836 16
5476 8836 16 36 256
B2, MC = 9773
1 25 625 841 8281
841 8281 1 25 625
25 625 841 8281 1
8281 1 25 625 841
625 841 8281 1 25
C2, MC = 24393
17 61 881 6317 17117
1097 13757 8837 41 661
8861 641 877 8537 5477
8317 257 5501 9461 857
6101 9677 8297 37 281


Pan Magic Square (7 x 7)

A1, MC = 1673
1 11 41 349 391 431 449
41 349 391 431 449 1 11
391 431 449 1 11 41 349
449 1 11 41 349 391 431
11 41 349 391 431 449 1
349 391 431 449 1 11 41
431 449 1 11 41 349 391
B1, MC = 718
14 20 26 54 84 90 430
90 430 14 20 26 54 84
54 84 90 430 14 20 26
20 26 54 84 90 430 14
430 14 20 26 54 84 90
84 90 430 14 20 26 54
26 54 84 90 430 14 20
A2, MC = 663847
1 121 1681 121801 152881 185761 201601
1681 121801 152881 185761 201601 1 121
152881 185761 201601 1 121 1681 121801
201601 1 121 1681 121801 152881 185761
121 1681 121801 152881 185761 201601 1
121801 152881 185761 201601 1 121 1681
185761 201601 1 121 1681 121801 152881
B2, MC = 204244
196 400 676 2916 7056 8100 184900
8100 184900 196 400 676 2916 7056
2916 7056 8100 184900 196 400 676
400 676 2916 7056 8100 184900 196
184900 196 400 676 2916 7056 8100
7056 8100 184900 196 400 676 2916
676 2916 7056 8100 184900 196 400
C2, MC = 868091
197 521 2357 124717 159937 193861 386501
9781 306701 153077 186161 202277 2917 7177
155797 192817 209701 184901 317 2081 122477
202001 677 3037 8737 129901 337781 185957
185021 1877 122201 153557 188677 208657 8101
128857 160981 370661 201797 401 797 4597
186437 204517 7057 8221 186581 121997 153281


Magic Square (8 x 8)

A1, MC = 1472
20 34 54 150 174 190 306 544
174 190 306 544 20 34 54 150
150 54 34 20 544 306 190 174
544 306 190 174 150 54 34 20
306 544 174 190 54 150 20 34
54 150 20 34 306 544 174 190
190 174 544 306 34 20 150 54
34 20 150 54 190 174 544 306
B1, MC = 2270
41 59 91 109 371 449 479 671
91 109 41 59 479 671 371 449
371 449 479 671 41 59 91 109
479 671 371 449 91 109 41 59
449 371 671 479 59 41 109 91
671 479 449 371 109 91 59 41
59 41 109 91 449 371 671 479
109 91 59 41 671 479 449 371
A2, MC = 482920
400 1156 2916 22500 30276 36100 93636 295936
30276 36100 93636 295936 400 1156 2916 22500
22500 2916 1156 400 295936 93636 36100 30276
295936 93636 36100 30276 22500 2916 1156 400
93636 295936 30276 36100 2916 22500 400 1156
2916 22500 400 1156 93636 295936 30276 36100
36100 30276 295936 93636 1156 400 22500 2916
1156 400 22500 2916 36100 30276 295936 93636
B2, MC = 1044248
1681 3481 8281 11881 137641 201601 229441 450241
8281 11881 1681 3481 229441 450241 137641 201601
137641 201601 229441 450241 1681 3481 8281 11881
229441 450241 137641 201601 8281 11881 1681 3481
201601 137641 450241 229441 3481 1681 11881 8281
450241 229441 201601 137641 11881 8281 3481 1681
3481 1681 11881 8281 201601 137641 450241 229441
11881 8281 3481 1681 450241 229441 201601 137641
C 2, MC = 1527168
2081 4637 11197 34381 167917 237701 323077 746177
38557 47981 95317 299417 229841 451397 140557 224101
160141 204517 230597 450641 297617 97117 44381 42157
525377 543877 173741 231877 30781 14797 2837 3881
295237 433577 480517 265541 6397 24181 12281 9437
453157 251941 202001 138797 105517 304217 33757 37781
39581 31957 307817 101917 202757 138041 472741 232357
13037 8681 25981 4597 486341 259717 497537 231277

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