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 2008-04-30, 18:12 #1 davar55     May 2004 New York City 102118 Posts Square of Primes Construct a 5 x 5 square containing distinct primes such that each row, column and diagonal sums to a distinct prime.
2008-04-30, 22:35   #2
petrw1
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"Wayne"
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29·32 Posts

Quote:
 Originally Posted by davar55 Construct a 5 x 5 square containing distinct primes such that each row, column and diagonal sums to a distinct prime.
Is it a magic square where every sum is the same?

 2008-04-30, 22:51 #3 davar55     May 2004 New York City 3·17·83 Posts A magic square of primes (where every sum is the same) is solved elsewhere (although it would be a perfectly good puzzle to re-solve). Here every sum is a different prime.
 2008-05-13, 18:07 #4 davar55     May 2004 New York City 3·17·83 Posts The original problem was perhaps too computationally simple to be interesting. The following additional condition adds an iota of complexity: The 25 distinct primes in the square should be the first 25 odd primes {3,5,7,...,97,101}. (I have a solution which wasn't hard to find by trial and error, so there must be many solutions; but plain brute force on the 25! such possible squares is obviously too computationally costly.) Last fiddled with by davar55 on 2008-05-13 at 18:08
 2008-05-17, 02:23 #5 lavalamp     Oct 2007 Manchester, UK 17×79 Posts Here's one: Code:  239 / / / 3, 5, 7, 11, 17 --- 43 13, 19, 29, 23, 43 --- 127 31, 67, 61, 47, 71 --- 277 53, 59, 41, 73, 37 --- 263 79, 83, 89, 97, 101 --- 443 | | | | | \ | | | | | \ | | | | | \ 179 233 227 251 269 257 Last fiddled with by lavalamp on 2008-05-17 at 02:26
 2008-05-17, 06:12 #6 S485122     Sep 2006 Brussels, Belgium 31758 Posts There is an error in your calculations : the last row total is of by 6. But the right number is prime so the solution stands :-) Jacob
 2008-05-17, 11:59 #7 lavalamp     Oct 2007 Manchester, UK 53F16 Posts Hm, I think I worked the total out right, but wrote it down wrong. It wasn't just a fluke, honest! ;)
 2008-05-19, 14:01 #8 m_f_h     Feb 2007 1B016 Posts Does the sequence a(n) = number of square matrices containing the first (2n+1)x(2n+1) odd primes, such that row, column and diagonal sums are distinct primes exist on OEIS ?
 2008-05-19, 14:57 #9 lavalamp     Oct 2007 Manchester, UK 17·79 Posts It would appear that there are an awful lot of these out there, so perhaps the challange should be to find a square with the lowest standard deviation of column/row/diagonal totals. I'll start the ball rolling with a slightly modified version of the last square I posted, with an s.d. of 84.51: Code:  239 / / / 3, 5, 7, 11, 17 --- 43 13, 19, 29, 23, 43 --- 127 31, 67, 61, 47, 71 --- 277 53, 59, 89, 73, 37 --- 311 79, 83, 41, 97, 101 --- 401 | | | | | \ | | | | | \ | | | | | \ 179 233 227 251 269 257 Last fiddled with by lavalamp on 2008-05-19 at 15:06
 2008-05-21, 12:54 #10 davar55     May 2004 New York City 3·17·83 Posts Here's another solution: 041 005 007 071 003 013 023 029 031 067 059 053 043 047 037 019 011 089 061 017 079 101 083 097 073 Rows: 127,163,239,197,433 Columns: 211,193,251,307,197 Diagonals: 241,167 (Standard deviation: 76.7) An alternative measure is simply mini-max: minimize the largest sum. By that measure, lavalamp's solution is a better one.

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