Problems & Puzzles: Puzzles

Puzzle 868. Magic squares 3x3 and palprimes

In memorial to Harvey Heinz, (1930-2013)

While solving the Puzzle 865, Jan van Delden used and reminded an old search of us.

In 1999 Carlos Rivera and Jaime Ayala published two magic squares 3x3 composed of nine palprimes each, in one of the pages of our esteemed friend Harvey Heinz :

 10797779701 14336063341 12568586521 14338283341 12567476521 10796669701 12566366521 10798889701 14337173341
 10915551901 12133533121 11527872511 12137973121 11525652511 10913331901 11523432511 10917771901 12135753121

We decided to remind that old search with the benefit of the velocities of the new now PCs at hand and constructing a totally new algorithm for this task.

If our new algorithm is correct, this time we found that there are NOT magic 3x3 squares for palprimes of odd lengths with 3, 5 & 7 digits.

The smallest magic square of these, starts in 9 digits.

This is the minimal one (minimal magic sum) for 9 digits:

127929721 149333941 135646531
145353541 137636731 129919921
139626931 125939521 147343741

The minimal one for 11 digits is this one:

10250405201 12614141621 11162726111
12254745221 11342424311 10430103401
11522122511 10070707001 12434443421

(Please notice that this is smaller than the smaller of the two sent to Harvey in 1999)

And so on...

Larger than these two, we were able to find at least one magic palprime square for 13, 15, 17, ... up to 31 digits.

Here is one magic square for 31 digits:

 3000000000085437345800000000003 3000000000431517151340000000003 3000000000243627263420000000003 3000000000411717171140000000003 3000000000253527253520000000003 3000000000095337335900000000003 3000000000263427243620000000003 3000000000075537355700000000003 3000000000421617161240000000003

For sure you can get larger magic 3x3 squares as these.

Q. Please send your larger magic 3x3 square for palprimes (larger quantity of digits).

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