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

%I A073523 #26 Nov 04 2018 14:47:07
%S A073523 67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,
%T A073523 163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251
%N A073523 The set of 36 consecutive primes that form a 6 X 6 pandiagonal magic square with the smallest magic constant (930).
%C A073523 There exist non-pandiagonal 6 X 6 magic squares composed of consecutive primes with smaller magic constant, the smallest being A073520(6) = 484.
%C A073523 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
%C A073523 See A320876 for the primes in the order in which they appear in the matrix. - _M. F. Hasler_, Oct 22 2018
%D A073523 Allan W. Johnson, Jr., Journal of Recreational Mathematics, vol. 23:3, 1991, pp. 190-191.
%D A073523 Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.
%H A073523 Harvey Heinz, <a href="http://www.magic-squares.net/primesqr.htm">Prime Magic Squares</a>
%H A073523 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A073523 The magic square is
%e A073523   [  67 193  71 251 109 239 ]
%e A073523   [ 139 233 113 181 157 107 ]
%e A073523   [ 241  97 191  89 163 149 ]
%e A073523   [  73 167 131 229 151 179 ]
%e A073523   [ 199 103 227 101 127 173 ]
%e A073523   [ 211 137 197  79 223  83 ]
%o A073523 (PARI) A073523=MagicPrimes(930,6) \\ See A073519 for MagicPrimes(). - _M. F. Hasler_, Oct 22 2018
%Y A073523 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).
%Y A073523 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.
%K A073523 nonn,fini,full
%O A073523 1,1
%A A073523 _N. J. A. Sloane_, Aug 29 2002
%E A073523 Edited by _Max Alekseyev_, Sep 24 2009
%E A073523 Edited by _M. F. Hasler_, Oct 29 2018