[Solved] A challenge- from physics with love  

Great challenge Saeed! For my first attempt I went with Pascal as it is quite easy to understand if you're new to coding. Though, it doesn't handle large numbers very well... which was the fatal flaw.

program Project1;

{$mode objfpc}{$H+}

uses sysUtils, strUtils;

var
binaryNum: string;
i, j: integer;

function BinToDec(bin: string): longint;
var
  i, j : integer;
begin
  j:= 1;
  BinToDec:= 0;
  for i:= length(bin) downto 1 do
    begin
      if bin[i]='1' then
        BinToDec+= j;
      j*= 2;
    end;
end;

function CheckPrime(n: longint): boolean;
var
  i: integer;
begin
  // Checks if n/i has a remainder of 0 where
  // 1 < i < n
  i:= 1;
  repeat
    inc(i);
  until (i=n-1) or (n mod i = 0);
  if i=n-1 then
    CheckPrime:= True
  else
    CheckPrime:= False;
end;

begin
  // Initialising binaryNum
  binaryNum:= '101';
  i:= 2;
  while True do
    begin
      // Output the number if prime
      if CheckPrime(BinToDec(binaryNum)) then
        writeln(binaryNum,' Position of 0: ',i);
      // Increase length by 2
      binaryNum:= binaryNum+'XX';
      // Format the number
      for j:= 1 to length(binaryNum) do
        if j=(length(binaryNum) div 2)+1 then
          binaryNum[j]:= '0'
        else
          binaryNum[j]:= '1';
      inc(i);
    end;
end.

The only output I had that was genuine was:

101 Position of 0: 2

The rest was hogwash, so I will be translating it to Java! Will update.

Hmm... I seem to be having an issue. If anyone knows how to use the StringBuilder data-type in Java, if you could tell me where this is going wrong, that would be fantastic.

public class PrimeHunt {
 public static int BinToDec(StringBuilder n) {
  int j = 1;
  int r = 0;
  for (int i=0; i<n.length(); i++) {
   if (n.charAt(i)=='1') {
    r+= j;
   }
  j*= 2;
  }
  return r;
 }
 
 public static boolean CheckPrime(int n) {
   for (int i=2; i<n; i++) {
    if (n % i == 0) {
     return false;
    }
   }
  return true;
 }
 
 public static void main(String[] args) {
  // TODO Auto-generated method stub
  StringBuilder binaryNum = new StringBuilder("101");
  while (1==1){
   if (CheckPrime(BinToDec(binaryNum))) {
    System.out.println(binaryNum);
    System.out.println(BinToDec(binaryNum));
   }
   binaryNum.append("XX");
   for (int j=0; j<binaryNum.length(); j++) {
    if (j==(binaryNum.length()/2)+1){
     binaryNum.setCharAt(j, '1');
    } else {
     binaryNum.setCharAt(j, '0');
    }
   }
  }
 }
}

May have to translate to another language... but that's the fun!