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A179440 The smallest magic constant of pan-diagonal magic squares which consist of distinct prime numbers.

%I A179440 #48 Aug 20 2025 21:01:37
%S A179440 240,395,450,733
%N A179440 The smallest magic constant of pan-diagonal magic squares which consist of distinct prime numbers.
%C A179440 Classic pan-diagonal magic squares exist for orders n > 3 not of the form 4k+2.
%C A179440 Non-traditional pandiagonal magic squares exist for all orders n > 3.
%C A179440 Bounds for further terms: a(8) <= 1248, a(9) <= 2025, a(10) <= 2850, a(11) <= 4195, a(12) <= 5544, a(13) <= 7597.
%H A179440 <a href="http://dxdy.ru/post423068.html#p423068">N. Makarova</a>, (in Russian)
%H A179440 <a href="http://e-science.ru/forum/index.php?showtopic=20405&amp;st=20">V. Pavlovsky</a>, (in Russian)
%H A179440 <a href="http://e-science.ru/forum/index.php?showtopic=20507&amp;st=80">S. Belyaev </a>, (in Russian)
%H A179440 Mutsumi Suzuki, <a href="http://mathforum.org/te/exchange/hosted/suzuki/MagicSquare.html">MagicSquare</a>
%H A179440 Al Zimmermann's Programming Contests, <a href="https://web.archive.org/web/20250328021437/http://azspcs.com/Contest/PandiagonalMagicSquares/FinalReport">Pandiagonal Magic Squares of Prime Numbers: Final Report</a>
%e A179440 a(5) = 395 (found by V. Pavlovsky)
%e A179440     5  73 127 137  53
%e A179440    37 167  17  71 103
%e A179440    83 101  13  67 131
%e A179440    43  31 197 113  11
%e A179440   227  23  41   7  97
%e A179440 .
%e A179440 a(6) = 450 (found by Radko Nachev)
%e A179440     3   5  89 137  67 149
%e A179440   127 163   7  29  11 113
%e A179440    31  23 167  59 157  13
%e A179440   107  97  43  53 131  19
%e A179440    73  79  41  71  47 139
%e A179440   109  83 103 101  37  17
%e A179440 .
%e A179440 a(7) = 733 (found by Jarek Wroblewski)
%e A179440     3   7 173 223  17 197 113
%e A179440   181 211  11  79 131  23  97
%e A179440    43  41 149  89 137 191  83
%e A179440   233 103 107  73 127  31  59
%e A179440    29 167 101  19 199  67 151
%e A179440     5  47 139 179 109  61 193
%e A179440   239 157  53  71  13 163  37
%Y A179440 Cf. A073523
%K A179440 more,nonn,bref
%O A179440 4,1
%A A179440 _Natalia Makarova_, Jul 14 2010
%E A179440 Correction for the third term with example given _Natalia Makarova_, Jul 21 2010
%E A179440 Link and example corrected by _Natalia Makarova_, Aug 01 2010
%E A179440 Edited by _Max Alekseyev_, Mar 15 2011
%E A179440 Bound for a(9) improved by _Alex Chernov_, Apr 23 2011
%E A179440 Bound for a(12) improved by _Natalia Makarova_, Jun 21 2011
%E A179440 Corrected a(6) from Radko Nachev, added by _Max Alekseyev_, May 28 2013
%E A179440 a(7) from Jarek Wroblewski and new bounds from Al Zimmermann's contest, added by _Max Alekseyev_, Oct 11 2013