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

240, 395, 450, 733

Offset: 4

Author

Natalia Makarova, Jul 14 2010

Keywords

• more
• nonn
• bref

Comments

Classic pan-diagonal magic squares exist for orders n > 3 not of the form 4k+2.

Non-traditional pandiagonal magic squares exist for all orders n > 3.

Bounds for further terms: a(8) <= 1248, a(9) <= 2025, a(10) <= 2850, a(11) <= 4195, a(12) <= 5544, a(13) <= 7597.

Examples

			a(5) = 395 (found by V. Pavlovsky)
    5  73 127 137  53
   37 167  17  71 103
   83 101  13  67 131
   43  31 197 113  11
  227  23  41   7  97
.
a(6) = 450 (found by Radko Nachev)
    3   5  89 137  67 149
  127 163   7  29  11 113
   31  23 167  59 157  13
  107  97  43  53 131  19
   73  79  41  71  47 139
  109  83 103 101  37  17
.
a(7) = 733 (found by Jarek Wroblewski)
    3   7 173 223  17 197 113
  181 211  11  79 131  23  97
   43  41 149  89 137 191  83
  233 103 107  73 127  31  59
   29 167 101  19 199  67 151
    5  47 139 179 109  61 193
  239 157  53  71  13 163  37
		

Links

• N. Makarova, (in Russian)
• V. Pavlovsky, (in Russian)
• S. Belyaev , (in Russian)
• Mutsumi Suzuki, MagicSquare
• Al Zimmermann's Programming Contests, Pandiagonal Magic Squares of Prime Numbers: Final Report

Crossrefs

Cf. A073523

Extensions

Correction for the third term with example given Natalia Makarova, Jul 21 2010

Link and example corrected by Natalia Makarova, Aug 01 2010

Edited by Max Alekseyev, Mar 15 2011

Bound for a(9) improved by Alex Chernov, Apr 23 2011

Bound for a(12) improved by Natalia Makarova, Jun 21 2011

Corrected a(6) from Radko Nachev, added by Max Alekseyev, May 28 2013

a(7) from Jarek Wroblewski and new bounds from Al Zimmermann's contest, added by Max Alekseyev, Oct 11 2013