smallest all-semiprime magic square

[Artur]

IN third squre is bug
Good is
4306...1858.....454,,,,,,,,,1018...3214...2386,,,,,,,,,,1294...1546...3778
1678...1894...3046,,,,,,,,,3574...2206.....838,,,,,,,,,,1366...2518...2734
..634...2866...3118,,,,,,,,,2026...1198...3394,,,,,,,,,,3958...2554.....106

All these numbers have to give rest 1 when divided by 3

Best Wishes
ARTUR


Dnia 25-12-2006 o 09:02:48 Jonathan Post <jvospost3 at gmail.com> napisał(a):

> Here's a semiprime magic cube, but it is not the smallest. The smallest
> order 3 prime cube is known, but not to me. The below is simply double  
> the
> elements of the Akio Suzuki 1977 prime cube shown in
> http://members.shaw.ca/hdhcubes/cube_prime.htm
> Thus it is very far indeed from coprimality within the rows, columns, or
> squares.
>
> 4306...1858.....454,,,,,,,,,1018...3214...2386,,,,,,,,,,1294...1436...3778
> 1678...1894...3046,,,,,,,,,3574...2206.....838,,,,,,,,,,1366...2518...2734
> ..634...2866...3118,,,,,,,,,2026...1198...3394,,,,,,,,,,3958...2554.....106
>
> The prime cube of which this is the double is described:
>
> "Also constructed by Akio Suzuki  in 1977 [1].  This cube has exactly the
> same characteristics as the above cube except it uses a smaller prime
> numbers.  Prime numbers used range from 53 to 2153. "
> "Each complement pair sums 2206 which is the sum of the smallest and  
> largest
> number used. In both cases, the middle number of the cube is this sum
> divided by 2. Both of these characteristics are common to all associated
> magic hypercubes. The constant is 3309."
>
>    *Addendum:* As a result of a computer search, Allen Wm, Johnson, Jr.  
> [2]
> confirmed that this cube has the smallest possible sum for an order 3  
> prime
> magic cube using distinct digits.
>
> [1] Gakuho Abe, *Related Magic Squares with Prime Elements*, JRM 10:2
> 1977-78, pp.96-97. Akio Suzuki order-3 and 4 cubes.
>
> [2] A. W. Johnson, Jr., *Solution to Problem 2617*, JRM 32:4, 2003-2004,  
> pp.
> 338-339
>
> [3] A. W. Johnson, Jr., *An Order 4 Prime Magic Cube,* JRM 18:1,  
> 1985-86, pp
> 5-7
>
>
> On 12/24/06, Jonathan Post <jvospost3 at gmail.com> wrote:
>>
>> Has progress been made since this article?
>>
>> Magic Tesseracts
>> Ivars Peterson
>> http://www.sciencenews.org/pages/sn_arc99/10_16_99/mathland.htm
>>
>> The smallest perfect magic tesseract is or order 16 (i.e. 16 x 16 x 16 x
>> 16).
>>
>> Are there prime magic tesseracts known? Can we construct semiprime magic
>> tesseracts analogous to the semiprime magic squares discussed earlier?
>>
>> Does the Peter Loly result on moment of intertia of magic squares and
>> magic cubes extend to magic tesseracts, with modifications since 4-D
>> rotation is about a plane rather than about an axis?
>>
>> On 12/24/06, David Wilson <davidwwilson at comcast.net > wrote:
>> >
>> >  Oh wait, I just had a "duh" moment.
>> >
>> > For a 3x3 magic square with center entry k, the row sum is 3k. So for  
>> a
>> > 3x3 prime magic square, the row sum is 3*prime, for a semiprime magic
>> > square, the row sum is 3*semiprime, for a parition number magic  
>> square, the
>> > row sum is 3*partition number, etc.
>> >
>> > Thus the 3x3 semiprime magic square cannot have a semiprime sum.
>> >
>>
>>