smallest 4x4 all-semiprime magic square

[Jonathan Post]

Ahem. the smallest all-semiprime magic square is

===
 4
===

Merry Christmas Eve Eve.

-- Dr. George Hockney



On 12/23/06, jonathan post <jvospost2 at yahoo.com> wrote:
>
> The Order 4 semiprime magic square is:
>
> 28213  23611  23257  27151
> 24319  26089  26443  28213
> 25735  24673  25027  26797
> 23965  27859  27505  22903
>
> The magic number (row, column, diagonal sum)
> = 102232 = 2^3 * 13 * 983.
> By another curious "base" concidence, 13 and 983 are
> emirps (primes which, read backwards, are still
> primes).
>
> These semiprime (k-almost prime) magic squares (cubes)
> raise new questions of enumeration, that can yield new
> sequences.  If, that is, anyone is interested.
>
> Best,
>
> Jonathan Vos Post
>
> p.s. The prime factorizations of the above 16 entries,
> in order, are:
>
> 1)  22903 = 37 * 619  (turn that 2nd one upside-down!)
> 2)  23257 = 13 * 1789 [13 colonies, constitution year)
> 3)  23611 = 7 * 3373
> 4)  23965 = 5 * 4793
> 5)  24319 = 83 * 293
> 6)  24673 = 11 * 2243
> 7)  25027 = 29 * 863
> 8)  28213 = 17 * 1493
> 9)  25735 = 5 * 5147
> 10) 26089 = 7 * 3727
> 11) 26443 = 31 * 853
> 12) 26797 = 127 * 211
> 13) 27151 = 19 * 1429
> 14) 27505 = 5 * 5501
> 15) 27859 = 13 * 2143
> 16) 28213 = 89 * 317
>
> Hard-core Magic Sqaure fans will recongize that my
> layout above parallels Durer's [1514) magic square.
>
> Best,
>
> Jonathan Vos Post
>
>
> --- jonathan post <jvospost2 at yahoo.com> wrote:
>
> >
> > --- Jonathan Post <jvospost3 at gmail.com> wrote:
> >
> > > Date: Sat, 23 Dec 2006 13:39:13 -0800
> > > From: "Jonathan Post" <jvospost3 at gmail.com>
> > > To: SeqFan <seqfan at ext.jussieu.fr>
> > > Subject: smallest all-semiprime magic square
> > > CC: jvospost2 at yahoo.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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