[ *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 |