[ April 1, 2002 ]
Magic Squares composed of only Palindromic Primes
Jean Claude Rosa [email]
There exist Magic Squares composed of only
palindromic primes all with 9 digits .
Jean Claude Rosa confirms this.
No solutions with 3, 5 or 7 digits exist.
| 147343741 | 125939521 | 139626931 | Magic Square |
|---|
| 129919921 | 137636731 | 145353541 | all numbers
 palprimes |
|---|
| 135646531 | 149333941 | 127929721 | by J. C. Rosa
April 1, 2002 |
|---|
The Magic Sum equals  3 * (middle cell) |
|---|
"Voici le carré magique suivant"
| 162484261 | 125474521 | 145494541 |
|---|
| 127494721 | 144484441 | 161474161 |
|---|
| 143474341 | 163494361 | 126484621 |
|---|
In total JCR found exactly 11 Palprimes Magic Squares with 9 digits.
Among these squares there is one that's quite nice:
| 177565771 | 131555131 | 157878751 |
|---|
| 135979531 | 155666551 | 175353571 |
|---|
| 153454351 | 179777971 | 133767331 |
|---|
Two days earlier JCR found a Palprimes Magic Square with 11 digits .
"J'espère que ce carré magique te fera plaisir !"
| 12434443421 | 10070707001 | 11522122511 | Magic Square |
|---|
| 10430103401 | 11342424311 | 12254745221 | all numbers
palprimes |
|---|
| 11162726111 | 12614141621 | 10250405201 | by J. C. Rosa
March 30, 2002 |
|---|
| The Magic Sum equals 3 * (middle cell) |
|---|
and which are all smaller than those found by Carlos Rivera
and Jaime Ayala (22/05/99) and that's on display at
Magic squares composed of only palprimes
"I'm really sorry for Carlos & Jaime."
Here is the next one !
Note that the middle cell determines the order.
| 11654345611 | 11023532011 | 11388488311 |
|---|
| 11089598011 | 11355455311 | 11621312611 |
|---|
| 11322422311 | 11687378611 | 11056565011 |
|---|
[ May 16, 2002 ]
"I (JCR) searched more Palprimes Magic Squares with 11 digits.
I got 89 solutions ( only for the central cell from
1*10^10 up to 2*10^10 ). A little nice collection...
Among these 89 squares I got, five times, two squares
with the same central cell and only once three squares
with the same central cell."
Here are those three squares :
| 18264546281 | 14428082441 | 16670707661 |
|---|
| 14860606841 | 16454445461 | 18048284081 |
|---|
| 16238183261 | 18480808481 | 14644344641 |
|---|
| 17744444771 | 14261716241 | 17357175371 |
|---|
| 16067176061 | 16454445461 | 16841714861 |
|---|
| 15551715551 | 18647174681 | 15164446151 |
|---|
| 17762726771 | 14054145041 | 17546464571 |
|---|
| 16238183261 | 16454445461 | 16670707661 |
|---|
| 15362426351 | 18854745881 | 15146164151 |
|---|
"Allez un petit dernier, assez joli :"
| 19738583791 | 15505850551 | 17935553971 |
|---|
| 15923632951 | 17726662771 | 19529692591 |
|---|
| 17517771571 | 19947474991 | 15714741751 |
|---|
JCR has also obtained the smallest Palprimes Magic Square,
each number in the square has 13 digits .
| 1026438346201 | 1000008000001 | 1013538353101 | Magic Square |
|---|
| 1000428240001 | 1013328233101 | 1026228226201 | all numbers
palprimes |
|---|
| 1013118113101 | 1026648466201 | 1000218120001 | by J. C. Rosa
March 30, 2002 |
|---|
| The Magic Sum equals 3 * (middle cell) |
|---|
Here are three follow ups !
| 1015646465101 | 1013107013101 | 1014822284101 |
|---|
| 1013701073101 | 1014525254101 | 1015349435101 |
|---|
| 1014228224101 | 1015943495101 | 1013404043101 |
|---|
| 1026946496201 | 1001702071001 | 1018824288101 |
|---|
| 1007702077001 | 1015824285101 | 1023946493201 |
|---|
| 1012824282101 | 1029946499201 | 1004702074001 |
|---|
| 1035676765301 | 1012851582101 | 1025438345201 |
|---|
| 1014417144101 | 1024655564201 | 1034893984301 |
|---|
| 1023872783201 | 1036459546301 | 1013634363101 |
|---|
And one more for the road !
| 1242207022421 | 1054028204501 | 1160116110611 |
|---|
| 1070026200701 | 1152117112511 | 1234208024321 |
|---|
| 1144118114411 | 1250206020521 | 1062027202601 |
|---|
A000129 