Problems & Puzzles: Puzzles

Puzzle 621. Puzzle 411 revisited

For our Puzzle 411 Giovanni Resta proposed a new mathematical object under study & sent the smallest of it:

a 3x3 magic square M such that if you change every entry k in M by p(k) you get a new magic square p(M), where p(k) is the k-th prime.

Remember that the minimal M object sent by Resta (that was rediscovered by JC Rosa, while solving the Resta's challenge) is this one:

        26199       25436      25819
        25438       25818      26198
        25817       26200      25437

and its associate:

       302573        292667        297629
       292679        297623        302567
       297617        302579        292673          

In that Puzzle 411 I added two questions -Q3 & Q4- that remain unsolved.

Thinking twice that pair of questions, now I see that solving Q3, Q4 is solved at the same time, which is not the case on the contrary. So, Q3 is harder than Q4, then again let's post Q4...

Q  . Find the smallest 3x3 magic square M such that p(M) is magic but every entry k in M is prime -or show that this object is impossible.

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