Problems & Puzzles: Puzzles

Puzzle 736. Associative Stanley squares of consecutive primes Natalia Makarova sent the following nice puzzle: Necessary definitions are given in the puzzles: http://www.primepuzzles.net/puzzles/puzz_681.htm http://www.primepuzzles.net/puzzles/puzz_717.htm n=2, d=18 (minimal) 5 7 11 13 n=3, d=4440084513 (minimal) 1480028189 1480028201 1480028213 1480028159 1480028171 1480028183 1480028129 1480028141 1480028153 This solution was obtained from the magic square of order 3 of consecutive primes. See http://www.magic-squares.net/primesqr.htm#A n=4, d=1282288088665523520 (not minimal?) 320572022166380833 320572022166380839 320572022166380843 320572022166380849 320572022166380893 320572022166380899 320572022166380903 320572022166380909 320572022166380851 320572022166380857 320572022166380861 320572022166380867 320572022166380911 320572022166380917 320572022166380921 320572022166380927 See http://www.primepuzzles.net/conjectures/conj_042.htm Questions: 1. Solution order of n = 4 is the minimal? 2. Find solutions for n>4.

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Max Alekseyev wrote on July 31, 2014:

The smallest set of 16 consecutive primes that can be arranged into an
4x4 associative Stanley antimagic square starts with 170693941183817.
This is example of such a square:

[170693941183817 170693941183859 170693941183907 170693941183949]
[170693941183847 170693941183889 170693941183937 170693941183979]
[170693941183861 170693941183903 170693941183951 170693941183993]
[170693941183891 170693941183933 170693941183981 170693941184023]

When the smallest prime subtracted from every element, it takes the form:
[ 0  42  90 132]
[30  72 120 162]
[44  86 134 176]
[74 116 164 206]

The square is obtained from the minimal 4x4 pandiagonal magic square
composed of the same primes. See Puzzle 723 and
http://oeis.org/A245721

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