mersenneforum.org Square of Primes
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2008-04-30, 18:12 #1 davar55     May 2004 New York City 108B16 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
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

2×32×277 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 108B16 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 5·7·112 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 3×5×7×13 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     "Jacob" Sep 2006 Brussels, Belgium 110111011102 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 3·5·7·13 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 1101100002 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 101010101012 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 5×7×112 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.

 Similar Threads Thread Thread Starter Forum Replies Last Post soumya Miscellaneous Math 1 2013-03-28 02:06 cmd cmd 118 2010-05-28 09:18 Fusion_power Puzzles 14 2008-04-25 11:37 davar55 Puzzles 34 2007-06-12 14:17 Zeta-Flux Math 16 2005-12-14 06:55

All times are UTC. The time now is 19:29.

Wed Jan 19 19:29:57 UTC 2022 up 180 days, 13:58, 0 users, load averages: 1.11, 1.54, 1.54

Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔