Java-Code

import java.util.*;
import java.lang.Math;
public class SumOfTwoSquares {
  public static void main(String[] args) {
    try {
      int number = Integer.parseInt(args[0]);          //  Read in the upper limit to find all prime numbers 
      System.out.println(allSquarePrime(number));      // that correspond to Fermat's theorem
    } catch(Exception e) {
      System.out.println(e);
    } finally {
      
    } // end of try
  }
  public static String allSquarePrime(int max) {   //  calculates all prime numbers that match the requirement
    String result ="";
    for (int i=5;i<max ;i++ ) {
      if (isPrime(i)&& i%4==1) {
        result += i +" "+getXY(i);
      } // end of if
    } // end of for
    return result;
  }
  public static boolean isPrime(int number) {     //  Method that checks whether a number is a prime number
    boolean isP = true;
    for (int i=2;i<=number/2 ;i++ ) {
      if (number%i == 0) {
        isP=false;  
      } // end of if
    } // end of for
    return isP;
  }
  public static String getXY(int number) {       // Method that calculates the squares of the given prime number
    String result="";
    ArrayList<Integer> searchList = new ArrayList<Integer>();
    for (int i=1;i*i<number ;i++ ) {                    // only checks possible squares for this prime number
      if (searchList.contains(i*i)) {
        result+=("("+((int)Math.sqrt(number-i*i))+","+(i)+")   ");
      } // end of if 
      else {
        searchList.add(number-i*i);                    //adds the associated summand of the current number to the array list
      } // end of if-else                              // for example : if the current number is 13 , you can only find the sum pair 
                                                       // between 1 and 3, because 4(square 16) is too big 
    } // end of for                                    // the assosiated summand for 1(square 1) would be 12, and for 2(square4)  
    return result;                                     // it would be 9, so we add those numbers to the list.
  }                                                    // If we reach 3(square 9) we will find the 9 in this lsit and we found the sum pair 

}