smallest all-semiprime magic square

[franktaw at netscape.net]

The smallest prime magic square is:

 17 89  71
113 59   5
 47 29 101

We can just double that, to get:

 34 178 142
226 118  10
 94  58 202

which is quite a bit smaller than your example.

Even if you want to exclude squares where the entries have a common 
divisor, your example looks suspiciously large to me.  And looking at 
A096003, it looks like you are assuming that your magic consists of 
numbers in arithmetic progression.  That is not a valid assumption.

Franklin T. Adams-Watters


-----Original Message-----
From: jvospost3 at gmail.com

   Using A096003 and A097824, here is the smallest all-semiprime magic 
square, which I just discovered today:

 ============
 1139 635 995
 779 923 1067
 851 1211 707
 ============

 In numerical order, these entries are:
 635 = 5*127
 707 = 7*101
 779 = 19*41
 851 = 23*37
 923 = 13*71
 995 = 5*199
 1067 = 11*97
 1139 = 17*67
 1211 = 7*173

  As I just noted in a submission to Prime Curios: 2769 is the sum of 
any row, column, or diagonal. Curiously, 2769 = 3 * 13 * 71, all three 
of which are primes when reversed (but that is too "base" for us here).

  Using A096003(16) = 28213, and A097824(16) = 354, one likewise has the 
smallest semiprime magic square of order 4.

  Using A096003(25) = 2012771, and A097824(25) = 9600, one likewise has 
the smallest semiprime magic square of order 5.

  I'm not sure if it's better to submit the finite full sequence 1139, 
635, 995, 779, 923, 1067,
  851, 1211, 707 for the order 3, and similarly for the order 4 and 
order 5; or give the sequence of row sums as a function of order n; or 
what.

 I don't know the order 6 or above.

  I also know the smallest order 3 of the 3-almost prime magic squares, 
and so forth, but these become "less" for most seqfans, I suspect.

  I admit to not yet having written down the smallest semiprime magic 
cbe, but the same method can be adapted...

 This is, new, is it not?

 Happy Hanukkah, Merry Christmas, etcetera,

 -- Jonathan Vos Post




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