FOR ROY: List of possible semiprime house numbers (between 5579 and 10000), where both prime factors are equal distant from their neighbors, by a distance of 2 and 6.

gistfile1.java

import java.util.ArrayList;
 
public class Address_Primes {
	private static ArrayList<Integer> possibilities = new ArrayList<Integer>();
	private static int minimum = 5579; //Roy's address is bigger than 5579
	
    public static boolean is_prime(int x){
    	for (int i = 2; i <= (Math.sqrt(x));i++){
    		if (x % i == 0){
    			return false;
    		}
    	}
    	return true;
    }	
    
    public static boolean equidistant_2(int x){
    	if (is_prime(x - 1) || is_prime(x + 1))
    		return false;
    	if (is_prime(x - 2) && is_prime(x + 2))
    		return true;
    	return false;
    }
 
	public static boolean equidistant_6(int x) {
		for (int i = 1; i < 6; i++) {
			if (is_prime(x - i) || is_prime(x + i)) {
				return false;
			}
		}
    	if (is_prime(x - 6) && is_prime(x + 6))
    		return true;
    	else return false;
	}
	
	public static ArrayList<Integer> enumerate_2(int max){
		ArrayList<Integer> equidistant = new ArrayList<Integer>();
		
		for(int i = 2; i < max;i++){
			if(is_prime(i) && equidistant_2(i))
				equidistant.add(i);
		}
		return equidistant;
	}
	
	public static ArrayList<Integer> enumerate_6(int max){
		ArrayList<Integer> equidistant = new ArrayList<Integer>();
		
		for(int i = 6; i < max;i++){
			if(is_prime(i) && equidistant_6(i))
				equidistant.add(i);
		}
		return equidistant;
	}
	
	public static ArrayList<Integer> possibilities(int max_2, int max_6){
		ArrayList<Integer> equidistant_2 = enumerate_2(max_2);
		ArrayList<Integer> equidistant_6 = enumerate_6(max_6);
		for(int i = 0; i < equidistant_2.size();i++)
			for(int j = 0; j < equidistant_6.size();j++)
				if((equidistant_2.get(i) * equidistant_6.get(j)) > minimum && (equidistant_2.get(i) * equidistant_6.get(j)) < 10000)
					Address_Primes.possibilities.add(equidistant_2.get(i) * equidistant_6.get(j));
		quicksort(0,Address_Primes.possibilities.size() - 1);
		return Address_Primes.possibilities;
	}
	
	public static String toString(ArrayList<Integer> arr_list){
		int size = arr_list.size();
		String re_string = "{ ";
		for (int i = 0; i < size - 1;i++){
			re_string = re_string + arr_list.get(i) + " , ";
		}
		re_string = re_string + arr_list.get(size - 1) + " }";
		return re_string;
	}
	
    public static void exchange(int i, int j){
        int t=Address_Primes.possibilities.get(i);
        Address_Primes.possibilities.set(i, Address_Primes.possibilities.get(j));
        Address_Primes.possibilities.set(j, t); 
   }
	
    private static void quicksort(int low, int high) {
	    int i = low, j = high;
	    int pivot = Address_Primes.possibilities.get((high+low)/2);
 
	    while (i <= j) {
 
	      while (Address_Primes.possibilities.get(i) < pivot) {
	        i++;
	      }
 
	      while (Address_Primes.possibilities.get(j) > pivot) {
	        j--;
	      }
 
	      if (i < j) {
	        exchange(i, j);
	        i++;
	        j--;
	      } else if (i == j) { i++; j--; }
	    }
 
	    if (low < j)
	      quicksort(low, j);
	    if (i < high)
	      quicksort(i, high);
	  }
    
    public static void main(String[] args) {
    	System.out.println(toString(possibilities(10000,10000)));  	
    }
}

Possible 4-digit house numbers greater than 5579: { 5615 , 5935 , 6115 , 6115 , 8735 , 8765 , 9535 }