Problems & Puzzles: Puzzles

Puzzle 944. Palprimes generating palprimes Carlos Rivera asks for palprimes generating palprimes according to the following model. Let P be a palprime. Then intertwine the digit D in P to generate other palprimes, for D=1, 2,  ... 9 My best solution is this P just for D = 1 to 5 P = 3273534353723 (13 digits) 3020703050304030503070203 (25 digits) 3121713151314131513171213 3222723252324232523272223 3323733353334333533373233 3424743454344434543474243 3525753555354535553575253 Q. Can you find a palprime producing palprimes for D going from 0 to 5<k<10?

---

Contribution came from Paul Cleary

***

Paul wrote on March 8, 2019:

I found a few more with d = 0 to 5 and 2 that had 8 of the 10 possible, but unfortunately they were not consecutive.  These are those 2, the {1,1,1,1,0,1,1,1,0,1} represents prime or not.

 

7808765306035678087

 

{1,1,1,1,0,1,1,1,0,1}

 

7080008070605030006000305060708000807

7181018171615131016101315161718101817

7282028272625232026202325262728202827

7383038373635333036303335363738303837

7484048474645434046404345464748404847 (C)

7585058575655535056505355565758505857

7686068676665636066606365666768606867

7787078777675737076707375767778707877

7888088878685838086808385868788808887 (C)

7989098979695939096909395969798909897

 

and

 

7792235971795322977

 

{1,1,1,1,0,1,1,1,0,1}

7070902020305090701070905030202090707

7171912121315191711171915131212191717

7272922222325292721272925232222292727

7373932323335393731373935333232393737

7474942424345494741474945434242494747 (C)

7575952525355595751575955535252595757

7676962626365696761676965636262696767

7777972727375797771777975737272797777

7878982828385898781878985838282898787 (C)

7979992929395999791979995939292999797

***

Giovanni Resta wrote on March 9, 2019:

(One of the two) partial solutions of Puzzle 944 (by Cleary) already appeared in Puzzle 72. 

***

---