Need help to find bug in factoring code

Question

I am coding a program to factor a number into is prime factors. The program works as follows:

1) Input a number that you wish to factor (I will refer to is as "inputNumber")

2) Test to see if you can divide inputNumber by 2,3,5 and 7 (first 4 prime numbers). if you can divide by any of these, then do so as many times as you can (i.e. 12 can be divided by 2 twice, after this, there is a remainder of 3) note every time I divide by a number, I store that number in an array list and I keep the remainder for further testing

3) Starting with i=11 (the next prime number) in a while loop, I do the following:

while (i < remainder+1) { 
divides by i? yes: store i, 
repeat until you cant divide by i. i=i+2, 
divides by i? yes: store i, repeat until you can't divide by i.
 i=i+4, same as before... i=i+2... 
and finally stop the loop at i=i+2 
} 

this way, every successful iteration of the while loop will divide the remainder by numbers finishing by 1,3,7,9. We do not need to test even numbers since we divided by 2 already, nor do we need to test the ones ending by 5 since we already divided by 5. In the end, we

This is a very neat algorithm since it its much much faster than factoring a number by testing one number after the other, in fact, you only need to test 40% of all numbers.

My question is: When I tried factoring 84738329279, a number picked randomly, it omits to put the last prime factor in the list, I can't quite figure this out. the only factors that show up are 41, 61 and 61. Can someone help me find what I'm doing wrong? here is my code:

import java.util.Scanner;
import java.math.BigInteger;

public class Test {

public static void main(String[] args) {
                    // create a scanner object for inputs
            Scanner in = new Scanner(System.in);

            // prompt user for number to factor
            System.out.print("enter a number to factor: ");
            String digits = in.next();
            BigInteger BigDigits = new BigInteger(digits);

            BigInteger[] results = factor.factorThis(BigDigits);


            System.out.print("Factors are ");
            for (int i=0; i<results.length;i++){
            System.out.print(results[i] + " ");
            }
            System.out.println("");
        }
}

import java.util.ArrayList;
import java.math.BigInteger;


public class factor {

// Returns the prime factors of the BigInteger number
public static BigInteger[] factorThis(BigInteger number) {

    BigInteger i = new BigInteger("11");
    ArrayList<BigInteger> divisors = new ArrayList<BigInteger>(0);

    BigInteger[] firstPrimes = new BigInteger[4];
    firstPrimes[0] = new BigInteger("2");
    firstPrimes[1] = new BigInteger("3");
    firstPrimes[2] = new BigInteger("5");
    firstPrimes[3] = new BigInteger("7");

    // loop that test for first 4 prime numbers
    for (int l=0;l<4;l++){
        while ((number.mod(firstPrimes[l])).compareTo(BigInteger.ZERO) == 0) {
            number = number.divide(firstPrimes[l]);
            divisors.add(firstPrimes[l]);
        }
    }


    // loop that factors only numbers finishing by 1,3,7,9
    while (i.compareTo(number) == -1){

        // check for ending by 1
        if ((number.mod(i)).compareTo(BigInteger.ZERO) == 0) {
            while (number.mod(i).compareTo(BigInteger.ZERO) == 0){
                number = number.divide(i);
                divisors.add(i);
            }
        }
        else if ((number.mod(i)).compareTo(BigInteger.ZERO) != 0){
            i=i.add(firstPrimes[0]);
        }

        // check for ending by 3
        if ((number.mod(i)).compareTo(BigInteger.ZERO) == 0) {
            while (number.mod(i).compareTo(BigInteger.ZERO) == 0){
                number = number.divide(i);
                divisors.add(i);
            }
        }
        else if ((number.mod(i)).compareTo(BigInteger.ZERO) != 0){
            i=i.add(firstPrimes[0].multiply(firstPrimes[0]));
        }

        //check for ending by 7
        if ((number.mod(i)).compareTo(BigInteger.ZERO) == 0) {
            while (number.mod(i).compareTo(BigInteger.ZERO) == 0){
                number = number.divide(i);
                divisors.add(i);
            }
        }
        else if ((number.mod(i)).compareTo(BigInteger.ZERO) != 0){
            i=i.add(firstPrimes[0]);
        }

        // check for ending by 9
        if ((number.mod(i)).compareTo(BigInteger.ZERO) == 0) {
            while (number.mod(i).compareTo(BigInteger.ZERO) == 0){
                number = number.divide(i);
                divisors.add(i);
            }
        }
        else if ((number.mod(i)).compareTo(BigInteger.ZERO) != 0){
            i=i.add(firstPrimes[0]);
        }
    }

    // store prime factors into a BigInt array
    String[] strArrayDivisors = divisors.toString().replaceAll("\\[", "").replaceAll("\\]","").replaceAll("\\s","").split(",");

    BigInteger[] BigIntDivisors = new BigInteger[strArrayDivisors.length];

    for(int j=0;j<strArrayDivisors.length;j++){
        BigIntDivisors[j] = new BigInteger(strArrayDivisors[j]);
    }

    // returns all factors of "number"
    return BigIntDivisors;

}   
}

Thanks in advance.

Answer 1

First, 84738329279 = 41 * 61 * 61 * 555439. Your 41, 61, and 61 are correct.

But when your algorithm terminates, you are left with the last prime number still in number. You'll need to add code that tests number at the end: if it's 1, then you're already finished, else it needs to add it to divisors so it gets printed later.