Problems & Puzzles: Puzzles

Puzzle 165.  Bye Mr. Suzuki

" I hope to see you again sometime and somewhere
 in another site of magic squares ",
Mr. Mutsumi Suzuki's closing Web-page

While not all the magic squares are such that its reversible ones are also magic squares, some of them really remain magic.

My friend Jaime Ayala not only introduced the subject but also produced the least of them

As you may suppose immediately I wanted to know if there are examples of prime-magic squares that:

a) their reversible are also magic
b) their reversible are also magic and prime

I offer an example-solution for a):

* as usual, primes are in blue

Question: 

Can you find a prime-magic square such that its reversible one is also prime-magic?

Solution:

Jean-Claude Rosa wrote (24/1/2002):

I have found  several solutions like you for question a) , by example:

 A)  17539     13729    15679         B)  93571     92731     97651

      13789     15649    17509               98731     94651     90571

      15619     17569    13759               91651     96571     95731

 
(numbers in bold letters are prime )

***

This solution from Rosa is very important (at least for me) because I was thinking that the central number had certain limiting value that... but forget it... all this I was thinking is evidently wrong...

***

J C Rosa smallest solution is:

and an improved solution (6 primes in the reverse magic square) from himself:

***

I  (C.R.) made again some search eliminating certain artificial conditions that I added for free previously to my code, and I have gotten one smaller solution with 6 primes in the reversible solution, than the provided by J.C. Rosa:

13469 11279 12689          96431 97211 98621
11699 12479 13259  --> 99611 97421 95231
12269 13679 11489          96221 97631 98411

(primes in bold)

***

J.C. Rosa found (27/1/02)  one solution with 7 primes:

167621 119291 155741          126761 192911 147551
135671 147551 159431 -->   176531 155741 134951
139361 175811 127481          163931 118571 184721

(primes in bold)

Later he reported other two, but not the following found by me, also with 7 primes:

175873 112213 175543       378571 312211 345571
154213 154543 154873       312451 345451 378451
133543 196873 133213       345331 378691 312331

***

J. C. Rosa has gotten (9/2/02) an almost complete solution, one in which the reversed matrix has only one composite number!

(primes in bold)

***

The game is over and the winner is... Jean Claude Rosa. The 3/3/2002 he found the 9 reversible, distinct and non-palindromic primes 3x3 magic square:

A big clap for this!

***