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

29790, 37530, 46002, 46050, 47502, 52290, 61110

Offset: 1

Author

Natalia Makarova, Jun 09 2015

Keywords

• nonn
• more

Comments

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.

All most-perfect magic squares are pandiagonal.

All pandiagonal magic squares of order 4 are most-perfect.

The magic constants of most-perfect magic squares of order 4 composed of distinct primes see A191533.

The minimal magic constant of most-perfect magic square of order 6 composed of distinct primes corresponds to a(1) = 29790, see A258082.

The seven terms shown have been verified by exhaustive search. - Natalia Makarova, Jun 09 2016

Examples

			a(2) = 37530 corresponds to the following most-perfect magic square:
   4919  9181  4049  6151  7949  5281
   9293  1627 10163  4657  6263  5527
   3833 10267  2963  7237  6863  6367
   6359  4561  7229  7591  3329  8461
   7853  6247  6983  3217 10883  2347
   5273  5647  6143  8677  2243  9547
a(3) = 46002 corresponds to the following most-perfect magic square:
   6053 14321  2417  6473 13901  2837
  10061   233 13697  8081  2213 11717
   5483 14891  1847  7043 13331  3407
   8861  1433 12497  9281  1013 12917
   7253 13121  3617  5273 15101  1637
   8291  2003 11927  9851   443 13487
		

Links

• Discussion at the scientific forum dxdy.ru, Magic squares (in Russian).
• N. Makarova, Puzzle 671: Most Perfect Magic Squares, Prime Puzzles & Problems.
• N. Makarova, Most-perfect magic squares of order 6
• Wikipedia, Most-perfect magic square

Crossrefs

Cf. A191533, A258082.