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December 11, 2016
Posted by **steve** on Monday, October 14, 2013 at 3:13am.

- Combinarorics -
**Steve**, Monday, October 14, 2013 at 4:14amwell, there are 10 primes, but I have no idea whether you can make a magic square with just primes.

- Combinarorics -
**Reiny**, Monday, October 14, 2013 at 8:33amMy basic 3 by 3 magic square looks like this using the numbers form 1 to 9:

8 1 6

3 5 7

4 9 2 for a sum of 15 for all its rows, columns, and diagonals

Without changing the sum, I can use symmetry to have different versions of that

e.g

2 7 6

9 5 1

4 3 8

There is also a magic square where the numbers form a fixed product of the numbers in the rows, columns, and diagonals

eg.

http://mathworld.wolfram.com/MultiplicationMagicSquare.html

but I don't think you were thinking of that.

For a "normal" magic square, the numbers form an arithmetic sequence.

so with a common difference of 1 we could use

1-9 , number of primes = 4 ,

2-10 , 4 primes

3-11 , 4primes

4-12 , 3 primes

....

19-27, 2 primes

There will be 19 of these magic squares, with the maximum number of primes in any one of them being 4

As soon as I make the common difference in the arithmetic sequence other than 1, e.g. 3

the numbers in the square would be multiples of that difference, hence no primes!

So primes can exist only if we have consecutive numbers.

I would say the max number of primes in any 3by3 magic square is 4

Steve mused if there was a magic square using only primes,

my guess is no, since the numbers must be in arithmetic sequence. - Combinarorics -
**steve**, Monday, October 14, 2013 at 8:50amit is also wrong. plss check it again

- Combinarorics -
**Steve**, Monday, October 14, 2013 at 12:12pmCan not a magic square be just a collection of random numbers that work magically? I was not aware that they had to be in arithmetic sequence.

- Combinarorics -
**Steve**, Monday, October 14, 2013 at 12:14pmIf we require an arithmetic sequence, then just lay a sliding scale over the numbers from 1-27 and see which string of 9 contains the most primes.

- @ Steve - Combinarorics -
**Reiny**, Monday, October 14, 2013 at 12:38pmSteve, back in the 80's when I was teaching a computer science course using GW-Basic on a "Trash -80" , I recall an assignment where using any number from 1 to 50, they were to find a magic square using a random number generator of size 5by5.

Of course the processor was so slow that we actually had to run the machines all night and wait to next day to get any results. We observed that for all results, the numbers were always consecutive numbers.

This does not prove it, but indicates strong indication it might be true.

You also stated that I was wrong in my reply, I can't find my error. - Combinatorics -
**Steve**, Monday, October 14, 2013 at 4:40pmNote that the assertion of error, came from "steve" not from "Steve"

Identity Theft!!!!

Back in the 60's when I was in HS, the CS class had to punch up their FORTRAN programs on cards, send them to Olympia for processing, and wait several days for the results. Now THAT's slow turnaround!

Luckily, I was a math geek back then, and had no real interest in computers. How times change... - Combinarorics -
**steve**, Monday, October 14, 2013 at 10:49pmso atlast what is the answer of my question? ???????