T-Shirt #4

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Problem Description

The fourth in the "T-Shirt" series:  

Back of T-Shirt:  "Smallest prime integer that remains prime when added to its reversal"

Front:  __ __ __ ?

Background & Techniques

Another beginner's level program that searches for the required number.  If the required prime is a three digit number (it is), then we are searching for the smallest prime number, abc, such that abc+cba is prime. 

There are about 30 user written lines of code here equally divided among three routines:

  • The IsPrime function returns true if the integer passed is prime, false if not prime.   
  • The Reverse function returns an integer with the digits of the input number reversed.  
  • And the SolveBtnCliick procedure, called when the user clicks the Solve button, loops with a control variable ranging from 13 to 999.    Each value is passed to IsPrime, if result is true the digits are reversed using Reverse function and the sum is passed to IsPrime.   Valid results are displayed in a Listbox.   

Here is the entire source code listing for the three subroutines:

{******* IsPrime *******}
function IsPrime(n:integer):boolean;  {Check is a number is prime}
var i:integer;
begin
    result:=true;
    for i:=2 to trunc(sqrt(n)) do {no need to check higher}
    if i*(i div n)i= n then   {is i a factor of n?}
    begin
        result:=false;
        break;
    end;
end;

{********* Reverse ********}
function Reverse(n:integer):integer;  {reverse the digits of an integer}
begin
    result:=0;
    while n>0 do
    begin
        result:=10*result + n mod 10;
        n:=n div 10;
    end;
end;

{********** SolveBtnClick ********}
procedure TForm1.SolveBtnClick(Sender: TObject);
var i,r:integer;
begin
    for i:= 13 to 999 do
    begin
        if IsPrime(i) then
        begin
            r:=Reverse(i);
            if IsPrime(i+r)
            then listbox1.items.add(inttostr(i) +' + '+inttostr(r)+' = '+inttostr(r+i));
        end; 
    end;
end;

Running/Exploring the Program 

Suggestions for Further Explorations

Smallest Palindromic prime?  (There's an IsPalindrome function in  T-Shirt #3 program)
Smallest palindromic prime which remains prime when added to its reversal?
Originally posted: May 30, 2002 Modified:February 18, 2016
 
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