smallest all-semiprime magic cube

[Artur]

What about smaller Magic Cube
{{717, 309, 75}, {169, 535, 397}, {215, 257, 629}}
{{279, 315, 507}, {595, 367, 139}, {227, 419, 455}}
{{105, 477, 519}, {337, 199, 565}, {659, 425, 17}}
With sum 1101

ARTUR


Dnia 25-12-2006 o 12:30:16 Artur <grafix at csl.pl> napisał(a):

> 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.
>>> >
>>>
>>>
>
>
>
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