A073523 The set of 36 consecutive primes that form a 6 X 6 pandiagonal magic square with the smallest magic constant (930).

67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251

Offset: 1

Author

N. J. A. Sloane, Aug 29 2002

Keywords

• nonn
• fini
• full

Comments

There exist non-pandiagonal 6 X 6 magic squares composed of consecutive primes with smaller magic constant, the smallest being A073520(6) = 484.

Pandiagonal means that not only the 2 main diagonals, but all other 10 diagonals also have the same sum, Sum_{i=1..6} A[i,M6(k +/- i)] = 930 for k = 1, ..., 6 and M6(x) = y in {1, ..., 6} such that y == x (mod 6). - M. F. Hasler, Oct 20 2018

See A320876 for the primes in the order in which they appear in the matrix. - M. F. Hasler, Oct 22 2018

Examples

			The magic square is
  [  67 193  71 251 109 239 ]
  [ 139 233 113 181 157 107 ]
  [ 241  97 191  89 163 149 ]
  [  73 167 131 229 151 179 ]
  [ 199 103 227 101 127 173 ]
  [ 211 137 197  79 223  83 ]
		

References

• Allan W. Johnson, Jr., Journal of Recreational Mathematics, vol. 23:3, 1991, pp. 190-191.
• Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.

Links

• Harvey Heinz, Prime Magic Squares
• Index entries for sequences related to magic squares

Crossrefs

Cf. A073519 and A320873 (3 X 3 magic square of consecutive primes), A073521 (consecutive primes of a 4 X 4 magic square), A245721 and A320874 (consecutive primes of a 4 X 4 pandigital magic square), A073522 (consecutive primes of a 5 X 5 magic square, not minimal and not pan-diagonal).

Cf. A256234: magic sums of 4 X 4 pandiagonal magic squares of consecutive primes, A073520: magic sums for n X n squares of consecutive primes.

Programs

PARI

A073523=MagicPrimes(930,6) \\ See A073519 for MagicPrimes(). - M. F. Hasler, Oct 22 2018

Extensions

Edited by Max Alekseyev, Sep 24 2009

Edited by M. F. Hasler, Oct 29 2018