WON plate129 | World!OfNumbers [ April 1, 2002 ]Magic Squares composed of only Palindromic Primesby 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. ``` 147343741125939521139626931Magic Square 129919921137636731145353541all numbers palprimes 135646531149333941127929721by J. C. RosaApril 1, 2002 The Magic Sum equals 3 * (middle cell)``` "Voici le carré magique suivant" ``` 162484261125474521145494541 127494721144484441161474161 143474341163494361126484621 ``` In total JCR found exactly  11  Palprimes Magic Squares with 9 digits. Among these squares there is one that's quite nice: ``` 177565771131555131157878751 135979531155666551175353571 153454351179777971133767331 ``` Two days earlier JCR found a Palprimes Magic Square with  11 digits . "J'espère que ce carré magique te fera plaisir !" ``` 124344434211007070700111522122511Magic Square 104301034011134242431112254745221all numbers palprimes 111627261111261414162110250405201by J. C. RosaMarch 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. ``` 116543456111102353201111388488311 110895980111135545531111621312611 113224223111168737861111056565011 ``` [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 : ``` 182645462811442808244116670707661 148606068411645444546118048284081 162381832611848080848114644344641 ``` ``` 177444447711426171624117357175371 160671760611645444546116841714861 155517155511864717468115164446151 ``` ``` 177627267711405414504117546464571 162381832611645444546116670707661 153624263511885474588115146164151 ``` "Allez un petit dernier, assez joli :" ``` 197385837911550585055117935553971 159236329511772666277119529692591 175177715711994747499115714741751 ``` JCR has also obtained the smallest Palprimes Magic Square, each number in the square has  13 digits . ``` 102643834620110000080000011013538353101Magic Square 100042824000110133282331011026228226201all numbers palprimes 101311811310110266484662011000218120001by J. C. RosaMarch 30, 2002 The Magic Sum equals 3 * (middle cell)``` Here are three follow ups ! ``` 101564646510110131070131011014822284101 101370107310110145252541011015349435101 101422822410110159434951011013404043101 102694649620110017020710011018824288101 100770207700110158242851011023946493201 101282428210110299464992011004702074001 103567676530110128515821011025438345201 101441714410110246555642011034893984301 102387278320110364595463011013634363101 ``` And one more for the road ! ``` 124220702242110540282045011160116110611 107002620070111521171125111234208024321 114411811441112502060205211062027202601 ``` A000129 Prime Curios! Prime Puzzle Wikipedia 129 Le nombre 129
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