素数幻方之最 江苏睢宁县供销总社 蔡宜文的素数幻方
1.十一阶素数幻方
2.十六阶素数幻方
3.二十阶素数幻方
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十一阶素数幻方 (用连续的 121个素数构成) |
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|
67 |
71 |
83 |
73 |
79 |
761 |
743 |
751 |
739 |
571 |
569 |
4507 |
|
797 |
787 |
769 |
773 |
757 |
89 |
97 |
127 |
103 |
107 |
101 |
4507 |
|
131 |
137 |
139 |
149 |
157 |
719 |
709 |
457 |
449 |
733 |
727 |
4507 |
|
701 |
691 |
677 |
673 |
683 |
163 |
151 |
269 |
277 |
109 |
113 |
4507 |
|
167 |
173 |
179 |
181 |
191 |
619 |
617 |
647 |
613 |
557 |
563 |
4507 |
|
641 |
643 |
653 |
607 |
631 |
193 |
199 |
257 |
223 |
197 |
263 |
4507 |
|
211 |
229 |
233 |
509 |
463 |
523 |
521 |
547 |
541 |
503 |
227 |
4507 |
|
599 |
601 |
577 |
587 |
317 |
283 |
241 |
251 |
499 |
281 |
271 |
4507 |
|
313 |
331 |
421 |
349 |
461 |
467 |
431 |
439 |
433 |
443 |
419 |
4507 |
|
401 |
353 |
379 |
367 |
359 |
307 |
311 |
373 |
337 |
659 |
661 |
4507 |
|
479 |
491 |
397 |
239 |
409 |
383 |
487 |
389 |
293 |
347 |
593 |
4507 |
|
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
4507 |
|
列和 |
行和 |
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日本幻方研究专家寺村周太郎先生在一九七九年十一月七日造出十阶素数幻方,用一○○个连续素数幻方构成。江苏睢宁县供销总社蔡宜文当然超过了这个记录。 |
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附录:121个素数
{67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 } 总和49577
| 16阶素数幻方
(用连续的256个素数构成) |
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| 13016 | ||||||||||||||||
| 31 | 37 | 43 | 41 | 47 | 59 | 61 | 53 | 1277 | 1279 | 1669 | 1667 | 1693 | 1697 | 1699 | 1663 | 13016 |
| 1657 | 1637 | 1627 | 1619 | 1621 | 1613 | 1289 | 1291 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 103 | 13016 |
| 101 | 107 | 109 | 113 | 167 | 127 | 131 | 139 | 1607 | 1609 | 1579 | 1597 | 1601 | 1583 | 1229 | 1217 | 13016 |
| 1571 | 1567 | 1559 | 1553 | 1549 | 1543 | 1171 | 1153 | 149 | 151 | 163 | 157 | 173 | 197 | 181 | 179 | 13016 |
| 191 | 193 | 199 | 211 | 223 | 227 | 257 | 229 | 1531 | 1523 | 1483 | 1487 | 1499 | 1129 | 1511 | 1123 | 13016 |
| 1063 | 1061 | 1493 | 1481 | 1489 | 1471 | 1459 | 1451 | 233 | 239 | 251 | 241 | 263 | 269 | 281 | 271 | 13016 |
| 277 | 283 | 293 | 311 | 307 | 317 | 313 | 337 | 1429 | 1447 | 971 | 983 | 1439 | 1433 | 1453 | 1423 | 13016 |
| 1427 | 1409 | 1399 | 1373 | 911 | 907 | 1361 | 1367 | 331 | 347 | 349 | 353 | 359 | 367 | 383 | 373 | 13016 |
| 379 | 421 | 397 | 409 | 401 | 419 | 389 | 439 | 1381 | 1307 | 1319 | 887 | 919 | 1301 | 1327 | 1321 | 13016 |
| 1303 | 1297 | 977 | 953 | 1283 | 1237 | 947 | 941 | 433 | 431 | 443 | 449 | 457 | 461 | 467 | 937 | 13016 |
| 479 | 491 | 487 | 523 | 499 | 509 | 827 | 1223 | 1213 | 1249 | 1231 | 1193 | 503 | 521 | 809 | 1259 | 13016 |
| 1201 | 1187 | 1181 | 1151 | 1163 | 1117 | 751 | 739 | 541 | 547 | 557 | 563 | 569 | 577 | 601 | 571 | 13016 |
| 587 | 593 | 641 | 607 | 613 | 787 | 1109 | 1091 | 599 | 619 | 1087 | 1093 | 1097 | 1103 | 617 | 773 | 13016 |
| 1069 | 1051 | 631 | 1033 | 1039 | 1031 | 1049 | 757 | 653 | 643 | 659 | 677 | 743 | 661 | 673 | 647 | 13016 |
| 683 | 691 | 1013 | 709 | 821 | 829 | 1021 | 1009 | 733 | 701 | 719 | 727 | 761 | 769 | 811 | 1019 | 13016 |
| 997 | 991 | 967 | 929 | 883 | 823 | 881 | 797 | 839 | 853 | 463 | 863 | 857 | 859 | 877 | 137 | 13016 |
| 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 | 13016 |
| 20阶素数幻方
(用连续的400个素数构成) |
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| 107 | 103 | 109 | 113 | 2903 | 2897 | 2887 | 2833 | 2879 | 2129 | 2843 | 2861 | 2857 | 2141 | 28184 |
| 2777 | 2767 | 2161 | 2179 | 137 | 131 | 139 | 127 | 151 | 149 | 163 | 167 | 157 | 179 | 28184 |
| 223 | 211 | 227 | 229 | 2011 | 2039 | 2851 | 2749 | 2753 | 2731 | 2729 | 2719 | 2741 | 2837 | 28184 |
| 2687 | 2693 | 2003 | 2017 | 241 | 239 | 251 | 233 | 271 | 263 | 277 | 269 | 257 | 281 | 28184 |
| 331 | 337 | 2677 | 2671 | 1889 | 2663 | 349 | 2621 | 2659 | 2647 | 2633 | 347 | 2657 | 1879 | 28184 |
| 2551 | 2549 | 1867 | 1861 | 373 | 359 | 383 | 353 | 379 | 367 | 389 | 397 | 401 | 409 | 28184 |
| 449 | 467 | 457 | 461 | 2543 | 2539 | 2521 | 2531 | 2503 | 2477 | 1847 | 2473 | 1871 | 2459 | 28184 |
| 2411 | 2393 | 1823 | 1873 | 463 | 479 | 491 | 487 | 499 | 509 | 503 | 521 | 523 | 577 | 28184 |
| 587 | 593 | 601 | 607 | 2399 | 2389 | 2383 | 1721 | 2377 | 2371 | 2357 | 2381 | 2347 | 1723 | 28184 |
| 2297 | 2287 | 2309 | 1657 | 659 | 613 | 647 | 599 | 631 | 641 | 617 | 643 | 619 | 653 | 28184 |
| 709 | 701 | 727 | 733 | 2273 | 2281 | 2293 | 2243 | 2267 | 1553 | 2251 | 2269 | 1543 | 2237 | 28184 |
| 2137 | 2153 | 1451 | 1459 | 739 | 743 | 821 | 761 | 787 | 757 | 773 | 769 | 751 | 857 | 28184 |
| 1531 | 853 | 863 | 887 | 2099 | 2131 | 2089 | 2063 | 827 | 2081 | 2113 | 2111 | 1559 | 2069 | 28184 |
| 1399 | 1427 | 2029 | 2083 | 859 | 877 | 947 | 911 | 929 | 881 | 883 | 919 | 907 | 997 | 28184 |
| 983 | 937 | 1061 | 1087 | 1979 | 991 | 1987 | 1319 | 1993 | 1913 | 1361 | 1933 | 1951 | 1949 | 28184 |
| 1523 | 1783 | 1831 | 1789 | 1049 | 1021 | 1063 | 1033 | 1091 | 1009 | 1019 | 1367 | 1051 | 1069 | 28184 |
| 1193 | 1117 | 1709 | 1777 | 1409 | 1877 | 1753 | 1453 | 1279 | 1747 | 1123 | 1759 | 1733 | 1801 | 28184 |
| 1429 | 1663 | 1433 | 1669 | 1151 | 1163 | 1217 | 1153 | 1187 | 1171 | 1201 | 1213 | 1181 | 1277 | 28184 |
| 1289 | 1583 | 1297 | 1609 | 1627 | 1259 | 1601 | 1621 | 1283 | 1307 | 1613 | 1619 | 1607 | 1303 | 28184 |
| 1571 | 1567 | 1549 | 1423 | 1381 | 1493 | 1511 | 1373 | 1439 | 1481 | 1489 | 1447 | 1471 | 1487 | 28184 |
| 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 | 28184 |
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400个连续素数 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903 |
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