Question

So I would call myself a fairly novice programmer as I focused mostly on hardware in my schooling and not a lot of Computer Science courses.

So I solved Problem 7 of Project Euler:

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10001st prime number?

I managed to solve this without problem in Java, but when I ran my solution it took 8 and change seconds to run. I was wondering how this could be optimized from a programming standpoint, not a mathematical standpoint.

Is the array looping and while statements the main things eating up processing time? And how could this be optimized? Again not looking for a fancy mathematical equation..there are plenty of those in the solution thread.

SPOILER My solution is listed below.

public class PrimeNumberList {

private ArrayList<BigInteger> primesList = new ArrayList<BigInteger>();

public void fillList(int numberOfPrimes) {
    primesList.add(new BigInteger("2"));
    primesList.add(new BigInteger("3"));
    while (primesList.size() < numberOfPrimes){
        getNextPrime();
    }
}

private void getNextPrime() {
    BigInteger lastPrime = primesList.get(primesList.size()-1);
    BigInteger currentTestNumber = lastPrime;
    BigInteger modulusResult;
    boolean prime = false;
    while(!prime){
        prime = true;
        currentTestNumber = currentTestNumber.add(new BigInteger("2"));
        for (BigInteger bi : primesList){
            modulusResult = currentTestNumber.mod(bi);
            if (modulusResult.equals(BigInteger.ZERO)){
                prime = false;
                break;
            }
        }
        if(prime){
            primesList.add(currentTestNumber);
        }
    }
}

public BigInteger get(int primeTerm) {
    return primesList.get(primeTerm - 1);
}

}

Answer 1

Since the 10001st prime number is not that big, you could start by using long instead of BigInteger. A BigInteger instance is a full-fledged Java Object and there is a lot of overhead in creating and manipulating them.