OFFSET
1,1
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
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
EXAMPLE
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 ]
PROG
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).
KEYWORD
nonn,fini,full
AUTHOR
N. J. A. Sloane, Aug 29 2002
EXTENSIONS
Edited by Max Alekseyev, Sep 24 2009
Edited by M. F. Hasler, Oct 29 2018
STATUS
approved