A073502 The smallest magic constant for n X n magic square with prime entries (regarding 1 as a prime).

111, 102, 213, 408, 699, 1114, 1681, 2416, 3355, 4514, 5937, 7626, 9635, 11986, 14691, 17818, 21373, 25394, 29873, 34926, 40511, 46664, 53445, 60898, 69045, 77888, 87473, 97850, 109065, 121126, 134113, 147982, 162759

Offset: 3

Author

N. J. A. Sloane, Aug 27 2002

Keywords

• nonn
• more

Comments

Until the early part of the twentieth century 1 was regarded as a prime (see A008578).

References

• W. S. Andrews and H. A. Sayles, The Monist (Chicago) for October 1913.
• H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 125, who quotes the Andrews-Sayles article as his source.

Links

• Yu. V. Chebrakov, Section 3.3. Smallest magic matrices of prime numbers in "Theory of Magic Matrices. Issue TMM-1.", 2008. (in Russian)
• N. Makarova 13 X 13 magic square. (in Russian)
• N. Makarova 14 X 14 magic square. (in Russian)
• Eric Weisstein's World of Mathematics, Prime Magic Square
• Index entries for sequences related to magic squares

Crossrefs

Cf. A073473 (for the n=3 square), A024351, A073520, A164843, A173079.

Extensions

Dudeney gives 36095/11 for n = 11 (an obvious typo) and 4514 for n = 12

a(3)-a(12) are confirmed/given by Chebrakov

a(15), a(17), a(22), a(35), and a(124)=9912840 from S. Tognon (cf. A173079)

a(13)-a(14), a(16), a(18)-a(21), a(23)-a(34) from N. Makarova

Edited by Max Alekseyev, Feb 11 2010