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%I #36 Aug 05 2015 05:25:33
%S 3505,990,4613,2040
%N Smallest magic constant of ultramagic squares of order n composed of distinct prime numbers.
%C A magic square is associative if the sum of any two elements symmetric about its center is the same. A magic square is pandiagonal if the sum of the numbers in any broken diagonal equals the magic constant. A magic square is ultramagic if it is associative and pandiagonal.
%C Ultramagic squares exist for orders n>=5.
%C The following bounds for the next terms are known: 12249<=a(9)<=13059, 4200<=a(10)<=46150, a(11)>=26521, a(12)>=8820, a(13)>=49439, a(14)>=16170, a(15)>=74595, a(16)>=21840.
%H Discussion at the scientific forum dxdy.ru, <a href="http://dxdy.ru/post1002869.html#p1002869">Devilish magic squares of primes</a> (in Russian)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Magic_square">Magic Square</a>
%e a(6)=990 corresponds to the following ultramagic square found by _Max Alekseyev_:
%e 103 59 163 233 139 293
%e 229 257 307 131 13 53
%e 283 17 67 173 181 269
%e 61 149 157 263 313 47
%e 277 317 199 23 73 101
%e 37 191 97 167 271 227
%e a(7)=4613 corresponds to the following ultramagic square found by _Natalia Makarova_:
%e 227 617 677 431 1217 1307 137
%e 1259 827 1061 509 521 167 269
%e 347 929 1187 17 557 719 857
%e 89 479 29 659 1289 839 1229
%e 461 599 761 1301 131 389 971
%e 1049 1151 797 809 257 491 59
%e 1181 11 101 887 641 701 1091
%e a(8)=2040 corresponds to the following ultramagic square found by _Natalia Makarova_:
%e 241 199 409 467 47 79 359 239
%e 421 137 7 53 487 179 317 439
%e 31 281 347 353 227 277 127 397
%e 449 197 109 379 491 337 11 67
%e 443 499 173 19 131 401 313 61
%e 113 383 233 283 157 163 229 479
%e 71 193 331 23 457 503 373 89
%e 271 151 431 463 43 101 311 269
%K nonn,more
%O 5,1
%A _Natalia Makarova_, Apr 20 2015
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