private static final BigInteger TWO = BigInteger.valueOf(2);
private static final BigInteger THREE = BigInteger.valueOf(3);
private static final BigInteger FIVE = BigInteger.valueOf(5);

public static ArrayList<BigInteger> primeDecomp(BigInteger n){
	if(n.compareTo(TWO) < 0) return null;
	ArrayList<BigInteger> factors = new ArrayList<BigInteger>();
	
	// handle even values
	while(n.and(BigInteger.ONE).equals(BigInteger.ZERO)){
		n = n.shiftRight(1);
		factors.add(TWO);
	}
	
	// handle values divisible by three
	while(n.mod(THREE).equals(BigInteger.ZERO)){
		factors.add(THREE);
		n = n.divide(THREE);
	}
	
	// handle values divisible by five
	while(n.mod(FIVE).equals(BigInteger.ZERO)){
		factors.add(FIVE);
		n = n.divide(FIVE);
	}
	
	// much like how we can skip multiples of two, we can also skip
	// multiples of three and multiples of five. This increment array
	// helps us to accomplish that
	int[] pattern = {4,2,4,2,4,6,2,6};
	int pattern_index = 0;
	BigInteger current_test = BigInteger.valueOf(7);
	while(!n.equals(BigInteger.ONE)){
		while(n.mod(current_test).equals(BigInteger.ZERO)){
			factors.add(current_test);
			n = n.divide(current_test);
		}
		current_test = current_test.add(BigInteger.valueOf(pattern[pattern_index]));
		pattern_index = (pattern_index + 1) & 7;
	}
	
	return factors;
}
