This is the Ranking of the “Pandiagonal Squares of Consecutive Primes” competition:
Pos
|
User
|
Points
|
Last Improvement
|
---|---|---|---|
1
|
primesmagicgames
|
3
|
16/12/2014
|
2
|
Natalia Makarova
|
1
|
23/09/2014
|
This is the Ranking of the “Pandiagonal Squares of Consecutive Primes” competition:
Pos
|
User
|
Points
|
Last Improvement
|
---|---|---|---|
1
|
primesmagicgames
|
3
|
16/12/2014
|
2
|
Natalia Makarova
|
1
|
23/09/2014
|
This competition is organized by Макарова Наталия (Natalia Makarova)
Magic square is called pandiagonal, if the sum of the numbers in each of the broken diagonal is the magic constant of the square.
For example – pandiagonal square of order 8 of prime numbers:
5 13 463 293 443 283 53 31 313 379 71 73 89 79 191 389 23 211 167 331 199 353 149 151 449 239 41 97 59 127 349 223 19 47 439 269 457 317 29 7 241 383 109 103 17 83 229 419 101 139 181 311 277 281 163 131 433 173 113 107 43 61 421 233 Magic constant of the square S = 1584
In the contest is required to construct pandiagonal squares of consecutive primes.
It is necessary to solve the problem for the orders n = 4 – 10.
Basic rule: solutions with known magic constants are not accepted.
n=4: Required to find solutions with magic constant S > 682775764735680
n=6: Required to find solutions with magic constant S > 930
170693941183817+ 0 116 132 164 162 134 30 86 74 42 206 90 176 120 44 72 S=682775764735680
See
http://oeis.org/A245721
http://dxdy.ru/post891839.html#p891839
320572022166380833+ 0 88 16 84 76 24 60 28 78 10 94 6 34 66 18 70 S = 1282288088665523520
See
http://dxdy.ru/post751928.html#p751928
http://www.primepuzzles.net/conjectures/conj_042.htm
Required to find solutions with magic constant S > 682775764735680.
67+ 0 126 4 184 42 172 72 166 46 114 90 40 174 30 124 22 96 82 6 100 64 162 84 112 132 36 160 34 60 106 144 70 130 12 156 16 S=930
Required to find solutions with magic constant S > 930.
Solutions should be introduced in a normalized form, plus dimension.
The first line must contains the dimension of problem (4, 5..10)
The second the normalized form of solution.
For example:
6 67: 0,126,4,184,42,172,72,166,46,114,90,40,174,30,124,22,96,82,6,100,64,162,84,112,132,36,160,34,60,106,144,70,130,12,156,16
Contestant receives one point for each new decision.
Solutions with the same magic constant are considered equal, even if they are not isomorphic.
Instituted a price to the participant who has won first place – $ 100 USA.
In cases of more people will have the same final score for the first positons, the price goes to the one that makes that score before the other.
If the winner will be the contestant from Russia, he will receive a prize in rubles at the official exchange rate on the last day of the competition.
The competition was taken from 23/09/2014 to 23/12/2014 but due to no winners (no one introduce a valid solution), it is now extended just for fun and not for price.
The competition Magic Cubes of Prime Numbers is over.
Thanks to all people that have partecipate.
The winner is Natalia, but price goes to Dmitry
The result is in this table:
Task
|
Dim.
|
User
|
Magic
|
Assoc.
|
Result
|
---|---|---|---|---|---|
1
|
4
|
Natalia Makarova
|
780
|
0
|
17 7 439 317
139 487 107 47 331 59 167 223 293 227 67 193 19 61 281 419 191 199 179 211 337 347 43 53 233 173 277 97 283 443 23 31 421 83 127 149 3 103 433 241 73 151 197 359 461 269 37 13 29 11 367 373 109 271 137 263 181 229 239 131 |
1
|
5
|
Dmitry Ezhov
|
5515
|
0
|
1063 1811 1109 331 1201 1171 673 1583 1361 727 479 1009 1031 1879 1117 2531 971 383 1367 263 271 1051 1409 577 2207 2011 373 739 1709 683 617 2749 1531 109 509 619 281 1697 1597 1321 797 811 839 1447 1621 1471 1301 709 653 1381 557 647 241 2239 1831 163 1637 1667 307 1741 2161 571 1103 773 907 761 1723 223 1999 809 1873 937 2281 197 227 1223 397 2693 1123 79 2267 97 631 1609 911 587 3221 1091 53 563 977 1663 13 389 2473 461 137 1087 2341 1489 661 2287 733 113 1721 1297 359 103 2129 1627 1669 433 593 1213 1607 449 347 4057 313 349 1439 2089 29 1747 211
|
1
|
6
|
Natalia Makarova
|
6030
|
0
|
13 59 1319 1439 1987 1213
1811 479 397 257 1759 1327 1973 383 839 1277 1091 467 1103 1949 1283 461 353 881 991 1259 499 1409 439 1433 139 1901 1693 1187 401 709 7 389 1777 1487 1913 457 1033 1861 19 641 1499 977 643 877 1597 1373 173 1367 1847 1193 71 1459 1297 163 947 89 2333 547 1051 1063 1553 1621 233 523 97 2003 809 1601 1291 557 31 1741 1567 151 73 1667 2129 443 1151 953 1723 587 757 859 787 283 1733 1303 701 1223 1447 2633 491 463 433 563 269 409 719 1453 1979 1201 1993 1999 1013 487 311 227 79 449 1889 1471 211 1931 347 1279 107 2017 617 1663 941 1061 1867 431 661 1069 887 1231 157 101 2531 1123 1783 11 997 1523 1699 17 1907 1873 313 1237 179 521 857 1559 2039 241 181 1153 373 911 593 43 2473 1637 223 1483 349 827 1361 1787 1181 67 1039 2909 5 829 1489 137 1697 773 1831 103 1301 109 317 823 1609 1871 683 1531 1613 1753 251 199 1543 1627 1171 733 919 37 1129 61 727 1549 1657 907 577 751 1511 601 1571 1019 797 1951 691 571 23 1997 |
1
|
7
|
Dmitry Ezhov
|
69811
|
0
|
9127 11083 631 9811 17551 12979 8629 8641 1579 18289 3463 15733 13789 8317 3229 18397 8179 277 13591 4549 21589 23293 223 23557 13933 6073 2539 193 5479 5653 8737 12289 7753 25303 4597 5119 11719 4327 20071 6553 6709 15313 14923 21157 6091 9967 2557 3943 11173 10987 7213 9067 10651 5953 9109 16831 4801 9241 16273 5623 9007 9283 15583 15649 14431 8221 5503 13381 10357 2269 4969 1663 19753 16141 10399 1063 15823 4339 20509 6451 9463 5743 9157 14149 12799 9883 8389 4933 23539 10069 199 16267 6871 1657 17497 1789 20773 4957 3607 13729 15241 7669 1543 24859 3163 12601 15607 1549 14797 2113 3637 19507 3019 7159 10867 6121 10567 17827 14251 20731 7573 331 997 21379 13159 5641 1861 8293 10723 19081 10159 5791 13903 21613 13807 6763 5407 16561 1237 4423 6379 3643 24337 15739 7489 3301 8923 13597 19603 5323 3253 16033 9199 2803 883 7789 12253 30493 1423 5227 11743 21937 457 21787 6247 18973 13 397 3583 12583 2719 9973 9151 16363 15439 22039 9343 5659 8377 271 12433 11689 4663 6343 11443 739 4159 22783 19681 3109 13693 10627 10729 19801 3793 8059 7369 5839 8839 20533 12451 1471 13309 25171 10531 6427 4051 7963 5557 10111 1999 5647 7993 16633 8461 24967 4111 12073 22063 16111 5107 13879 439 139 16087 17341 12097 6529 8353 2347 7057 1699 4027 1297 11257 8527 15643 27361 5413 4363 17047 5701 10177 19387 7723 14293 6907 11491 5857 13633 1741 15889 11863 9613 7069 9043 24469 6661 1093 6397 8599 10477 17239 2089 5827 19183 3631 9733 6733 8893 2713 34369 3739 7417 5821 22573 5209 12739 7039 9013 7351 14401 4789 20011 9091 11497 2671 18859 14737 6679 3559 5077 2677 18223 10831 5437 19219 12037 2647 10453 9187 5851 15451 7951 2341 9103 25657 3457 17581 15121 2287 17791 2749 6271 8011 1531 15973 607 14767 6217 1879 28837 12589 2851 3571 8863 24793 7741 9403 16567 9631 32803 7393 1381 1873 163 4861 5347 3373 6619 22921 15937 10753
|
2
|
4
|
Natalia Makarova
|
1260
|
630
|
23 521 433 283
373 29 457 401 587 139 11 523 277 571 359 53 263 379 557 61 613 13 131 503 317 449 31 463 67 419 541 233 397 89 211 563 167 599 181 313 127 499 617 17 569 73 251 367 577 271 59 353 107 619 491 43 229 173 601 257 347 197 109 607 |
2
|
5
|
Natalia Makarova
|
54515
|
21806
|
14347 21163 9349 4099 5557
3793 9883 20899 9463 10477 6379 15739 12919 10369 9109 13627 3673 3019 21397 12799 16369 4057 8329 9187 16573 5113 11149 9397 19087 9769 17443 4603 283 18307 13879 16183 3847 17359 1483 15643 14563 13933 9043 2539 14437 1213 20983 18433 13099 787 8803 877 18919 12757 13159 16903 20353 1783 739 14737 13093 3169 10903 18637 8713 7069 21067 20023 1453 4903 8647 9049 2887 20929 13003 21019 8707 3373 823 20593 7369 19267 12763 7873 7243 6163 20323 4447 17959 5623 7927 3499 21523 17203 4363 12037 2719 12409 10657 16693 5233 12619 13477 17749 5437 9007 409 18787 18133 8179 12697 11437 8887 6067 15427 11329 12343 907 11923 18013 16249 17707 12457 643 7459 |
2
|
6
|
Natalia Makarova
|
19800
|
6600
|
883 3697 5591 4243 233 5153
1117 5923 4457 1031 4799 2473 5387 977 4289 2273 5507 1367 4447 2861 179 6121 743 5449 6269 5323 863 1549 2777 3019 1697 1019 4421 4583 5741 2339 1783 6373 239 47 6007 5351 19 53 3643 4159 5477 6449 31 131 1667 5413 6037 6521 6211 3673 5113 2087 1523 1193 5227 3371 4349 6091 733 29 6529 6199 4789 2003 23 257 397 211 3299 5861 5981 4051 1949 127 3463 3209 4561 6491 3691 1979 5419 1097 1327 6287 3517 6337 3491 3167 821 2467 3917 6143 3187 3923 2593 37 6329 5003 941 2543 4517 467 6133 2083 4057 5659 1597 271 6563 4007 2677 3413 457 2683 4133 5779 3433 3109 263 3083 313 5273 5503 1181 4621 2909 109 2039 3391 3137 6473 4651 2549 619 739 3301 6389 6203 6343 6577 4597 1811 401 71 6571 5867 509 2251 3229 1373 5407 5077 4513 1487 2927 389 79 563 1187 4933 6469 6569 151 1123 2441 2957 6547 6581 1249 593 6553 6361 227 4817 4261 859 2017 2179 5581 4903 3581 3823 5051 5737 1277 331 1151 5857 479 6421 3739 2153 5233 1093 4327 2311 5623 1213 4127 1801 5569 2143 677 5483 1447 6367 2357 1009 2903 5717 |
Here are the best solution arrived after the ending of the competition:
Task
|
Dim.
|
User
|
Magic
|
Assoc.
|
Result
|
---|---|---|---|---|---|
1
|
5
|
Michael Huerter
|
2735
|
0
|
223 61 1439 881 131 73 1033 277 199 1153 1429 829 271 97 109 991 379 641 701 23 19 433 107 857 1319 11 1019 191 937 577 1697 523 59 409 47 31 127 1109 491 977 89 599 643 311 1093 907 467 733 587 41 877 499 29 269 1061 383 607 137 1259 349 787 3 547 571 827 431 853 1201 149 101 257 773 821 487 397 1307 227 769 419 13 503 241 193 617 1181 151 1049 569 593 373 313 557 233 823 809 461 661 971 283 359 317 929 307 229 953 79 331 2069 251 5 337 727 239 983 449 911 347 17 751 709 1091 401 103 521 619
|
1
|
6
|
Natalia Makarova
|
5670
|
0
|
971 761 1801 367 157 1613
1447 379 491 1031 569 1753 1033 1667 1709 281 877 103 1117 1777 419 457 1607 293 461 23 787 1723 797 1879 641 1063 463 1811 1663 29 607 409 719 1877 1627 431 1543 1039 31 887 1823 347 599 439 2311 383 647 1291 233 353 557 2371 499 1657 1229 1949 881 139 811 661 1459 1481 1171 13 263 1283 937 149 1303 677 983 1621 1553 97 307 2069 1307 337 727 2267 523 317 673 1163 653 967 1451 271 1091 1237 1531 449 1499 1123 709 359 269 1741 587 1213 907 953 1277 1693 19 1289 829 563 593 53 2333 751 643 1297 1423 991 107 373 2309 467 311 2423 571 659 127 1579 739 313 769 1997 701 1151 1327 197 1871 601 1061 613 17 1831 401 1381 1847 193 397 2591 1109 73 7 1493 101 83 839 2707 151 1789 1759 37 1201 479 2063 131 1699 1069 631 521 1559 191 1697 59 1489 509 43 1873 1861 827 1427 79 227 1249 137 1511 1399 859 1321 443 1787 223 181 1609 1013 857 1597 113 1471 1433 283 773 11 1867 1103 167 1093 1429 277 1129 89 1523 1733 919 |
1
|
7
|
Michael Huerter
|
18053
|
0
|
4889 5659 3373 443 547 263 2879 859 1481 4357 3889 631 3769 3067 941 643 131 2549 5927 3313 4549 997 2663 3733 2633 2153 4967 907 2417 3433 3221 739 4649 457 3137 5867 293 2969 1637 3989 2441 857 2083 3881 269 6163 157 2843 2657 1931 23 1213 2837 5657 4261 2131 1039 4801 3391 4177 1913 2161 571 5227 3023 4057 1831 823 2239 853 1531 1283 1217 1151 4787 4441 3643 3719 3229 2939 3347 2141 1759 919 2999 1933 2069 4519 1033 1571 3929 1607 3761 3167 191 1699 1621 6007 4759 4481 487 2311 1061 2711 2243 683 809 2833 109 6917 6473 229 349 4793 3169 4909 673 4099 61 6491 1489 1667 5233 1483 1619 71 4079 1289 2557 1063 5021 2677 1367 401 1861 5563 967 991 277 7993 1291 3331 1777 3461 1907 197 6089 1009 2423 4861 4423 3499 181 1657 1511 6673 107 2371 19 1523 5849 6529 3911 1709 79 2087 2137 1601 1373 2333 5297 2579 41 3467 2963 2383 1163 271 2143 1873 5653 4567 167 1399 3527 5647 5783 953 577 5081 151 2281 811 4751 4139 839 199 4483 2801 1453 101 3779 5237 5003 1433 2293 1031 2203 937 5153 2351 2713 1847 4789 3251 1783 1319 2213 3109 2671 173 5323 2207 2357 2179 2957 2621 6779 491 2887 139 2749 3329 1693 1109 563 6143 2467 3359 29 4127 2719 6121 317 1381 977 227 5107 4349 2797 3299 1297 5839 89 1951 4447 1499 3041 1187 1427 2251 1549 1459 2819 431 8117 251 6389 2447 601 3557 1069 3739 2617 1249 5351 3623 409 2027 2777 2689 6761 239 2273 4111 1237 743 4253 1087 1409 1301 2861 6949 193 4289 757 211 2237 4391 3559 2609 3119 2767 3121 2029 4871 149 1997 1229 719 5591 2437 2473 4051 1553 5197 787 1021 5683 709 283 4373 659 4733 1093 359 3469 2593 5147 3181 2477 1993 1901 1583 5431 1487 379 5813 5023 3407 557 1987 887
|
This is the Ranking of the “Magic Cubes of Prime Numbers” competition:
Pos
|
User
|
Points
|
Last Improvement
|
---|---|---|---|
1
|
Natalia Makarova
|
6.3404
|
08/06/2014
|
2
|
Dmitry Ezhov
|
3.0154
|
17/05/2014
|
3
|
Jarek
|
0.4615
|
23/04/2014
|
This competition is organized by Макарова Наталия (Natalia Makarova)
A magic cube is the 3-dimensional equivalent of a magic square, that is, a number of integers arranged in an n x n x n pattern such that the sum of the numbers on each row, each column, each pillar and the four main space diagonals is equal to a single number, the so-called magic constant (S) of the cube.
For example – the classic magic cube of order 3:
18 23 1 22 3 17 2 16 24 20 7 15 9 14 19 13 21 8 4 12 26 11 25 6 27 5 10 S=42
The magic cube is associative (central symmetric) if the sum of any 2 numbers, symmetrically located relative to the center of the cube, is equal to a single number, the so-called constant of associativity of the cube.
For example – an associative magic cube of order 5 of arbitrary natural numbers:
43357 31873 31741 38041 43423 43567 29593 15685 47515 52075 6547 47647 75373 50713 8155 43513 39643 31723 31687 41869 51451 39679 33913 20479 42913 34933 34051 41611 34297 43543 35317 37327 42247 37423 36121 36277 43123 32311 42211 34513 40807 41401 32143 34183 39901 41101 32533 40123 40321 34357 36667 32563 38371 37561 43273 40573 36637 43621 33793 33811 37531 39841 37687 35533 37843 41563 41581 31753 38737 34801 32101 37813 37003 42811 38707 41017 35053 35251 42841 34273 35473 41191 43231 33973 34567 40861 33163 43063 32251 39097 39253 37951 33127 38047 40057 31831 41077 33763 41323 40441 32461 54895 41461 35695 23923 33505 43687 43651 35731 31861 67219 24661 1 27727 68827 23299 27859 59689 45781 31807 31951 37333 43633 43501 32017 S=188435
Magic cubes of order 3 are simple magic cubes.
All magic cubes of order 3 are associative (see [3], [7]).
This competition requires to make magic cubes of distinct primes:
For example – magic cube of order n = 3 of prime numbers:
1061 3167 863 2243 431 2417 1787 1493 1811 2447 23 2621 1871 1697 1523 773 3371 947 1583 1901 1607 977 2963 1151 2531 227 2333 S = 5091
There are thus 8 distinct problems.
All prime numbers must be less than 2*10^9 (exceptions are made for n = 7).
Solutions can have magic constants S1> S2> S3> …> Smin.
Two solutions of task #1 with equal magic constants S are considered equal, even if they are not equivalent.
This rule also applies to the solutions of the task #2.
Note:
Solutions are called equivalent if they are obtained by rotations and reflections.
The first line is written task number (1 or 2) and the order of the cube (4, 5, 6, 7), separated by commas. For example, in the task 1 for n = 4 in the first row must be written: 1,4
The second line is recorded magic cube elements, separated by commas, for example:
1061,3167,863,2243,431,2417,1787,1493,1811,2447,23,2621,1871,1697,1523,773,3371,947,1583,1901,1607,977,2963,1151,2531,227,2333
In this line you can insert a “new line” in any place, for example:
1061,3167,863,2243,431,2417,1787,1493, 1811,2447,23,2621,1871,1697,1523,773, 3371,947,1583,1901,1607,977,2963,1151,2531,227,2333
Policies is the same for both tasks. Scores received by the participant for solving task #1 and task #2 are summarized.
Let solutions contestants A, B, C, D, E for n = 3 (although the order is not included in the contest problem, but the real values are known magic constants [7]).
Established a prize to the participant who has won first place – $100 (U.S.)
Notes:
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