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%I #38 Jan 09 2021 02:39:12
%S 240,395,450,733
%N The smallest magic constant of pan-diagonal magic squares which consist of distinct prime numbers
%C Classic pan-diagonal magic squares exist for orders n > 3 not of the form 4k+2.
%C Non-traditional pandiagonal magic squares exist for all orders n > 3.
%C Bounds for further terms: a(8) <= 1248, a(9) <= 2025, a(10) <= 2850, a(11) <= 4195, a(12) <= 5544, a(13) <= 7597.
%H <a href="http://dxdy.ru/post423068.html#p423068">N. Makarova</a>, (in Russian)
%H <a href="http://e-science.ru/forum/index.php?showtopic=20405&st=20">V. Pavlovsky</a>, (in Russian)
%H <a href="http://e-science.ru/forum/index.php?showtopic=20507&st=80">S. Belyaev </a>, (in Russian)
%H Mutsumi Suzuki, <a href="http://mathforum.org/te/exchange/hosted/suzuki/MagicSquare.html">MagicSquare</a>
%H Al Zimmermann's Programming Contests, <a href="http://www.azspcs.net/Contest/PandiagonalMagicSquares/FinalReport">Pandiagonal Magic Squares of Prime Numbers: Final Report</a>
%e a(5) = 395 (found by V. Pavlovsky)
%e 5 73 127 137 53
%e 37 167 17 71 103
%e 83 101 13 67 131
%e 43 31 197 113 11
%e 227 23 41 7 97
%e .
%e a(6) = 450 (found by Radko Nachev)
%e 3 5 89 137 67 149
%e 127 163 7 29 11 113
%e 31 23 167 59 157 13
%e 107 97 43 53 131 19
%e 73 79 41 71 47 139
%e 109 83 103 101 37 17
%e .
%e a(7) = 733 (found by Jarek Wroblewski)
%e 3 7 173 223 17 197 113
%e 181 211 11 79 131 23 97
%e 43 41 149 89 137 191 83
%e 233 103 107 73 127 31 59
%e 29 167 101 19 199 67 151
%e 5 47 139 179 109 61 193
%e 239 157 53 71 13 163 37
%Y Cf. A073523
%K more,nonn,bref
%O 4,1
%A _Natalia Makarova_, Jul 14 2010
%E Correction for the third term with example given _Natalia Makarova_, Jul 21 2010
%E Link and example corrected by _Natalia Makarova_, Aug 01 2010
%E Edited by _Max Alekseyev_, Mar 15 2011
%E Bound for a(9) improved by Alex Chernov, Apr 23 2011
%E Bound for a(12) improved by _Natalya Makarova_, Jun 21 2011
%E Corrected a(6) from Radko Nachev, added by _Max Alekseyev_, May 28 2013
%E a(7) from Jarek Wroblewski and new bounds from Al Zimmermann's contest, added by _Max Alekseyev_, Oct 11 2013
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