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A258755 The magic constants of most-perfect magic squares of order 6 composed of distinct prime numbers.

%I A258755 #26 Jun 10 2016 10:37:58
%S A258755 29790,37530,46002,46050,47502,52290,61110
%N A258755 The magic constants of most-perfect magic squares of order 6 composed of distinct prime numbers.
%C A258755 A magic square of order n = 2k is most-perfect if the following two conditions hold: (i) every 2 X 2 subsquare (including wrap-around) sums to 2T; and (ii) any pair of elements at distance k along a diagonal or a skew diagonal sums to T, where T = S/k, S is the magic constant.
%C A258755 All most-perfect magic squares are pandiagonal.
%C A258755 All pandiagonal magic squares of order 4 are most-perfect.
%C A258755 The magic constants of most-perfect magic squares of order 4 composed of distinct primes see A191533.
%C A258755 The minimal magic constant of most-perfect magic square of order 6 composed of distinct primes corresponds to a(1) = 29790, see A258082.
%C A258755 The seven terms shown have been verified by exhaustive search. - _Natalia Makarova_, Jun 09 2016
%H A258755 Discussion at the scientific forum dxdy.ru, <a href="http://dxdy.ru/post976822.html#p976822">Magic squares</a> (in Russian).
%H A258755 N. Makarova, <a href="http://www.primepuzzles.net/puzzles/puzz_671.htm">Puzzle 671: Most Perfect Magic Squares</a>, Prime Puzzles & Problems.
%H A258755 N. Makarova, <a href="/A258755/a258755.txt">Most-perfect magic squares of order 6</a>
%H A258755 Wikipedia, <a href="http://en.wikipedia.org/wiki/Most-perfect_magic_square">Most-perfect magic square</a>
%e A258755 a(2) = 37530 corresponds to the following most-perfect magic square:
%e A258755    4919  9181  4049  6151  7949  5281
%e A258755    9293  1627 10163  4657  6263  5527
%e A258755    3833 10267  2963  7237  6863  6367
%e A258755    6359  4561  7229  7591  3329  8461
%e A258755    7853  6247  6983  3217 10883  2347
%e A258755    5273  5647  6143  8677  2243  9547
%e A258755 a(3) = 46002 corresponds to the following most-perfect magic square:
%e A258755    6053 14321  2417  6473 13901  2837
%e A258755   10061   233 13697  8081  2213 11717
%e A258755    5483 14891  1847  7043 13331  3407
%e A258755    8861  1433 12497  9281  1013 12917
%e A258755    7253 13121  3617  5273 15101  1637
%e A258755    8291  2003 11927  9851   443 13487
%Y A258755 Cf. A191533, A258082.
%K A258755 nonn,more
%O A258755 1,1
%A A258755 _Natalia Makarova_, Jun 09 2015