Need a more efficient algorithm for prime numbers.

Here is my current algorithm, the TimeExec is just a class to print out how long it takes to run the code:

Code java:

---

public class Primes {
 
	/**
	 * Get a set of prime numbers.
	 * @param no the number of primes to create
	 * @return an array containing the requested number
	 * of primes
	 */
	public static int[] getPrimes(int no) {
		int[] primes = new int[no];
		int primeInx = 0;
		int i = 2;
 
		if (primeInx < no) {
			primes[primeInx++] = 1;
		}
 
		while (primeInx < no) {
			boolean prime = true;
			for (int j = 2; j < i; j++) {
 
				if (i == i / j * j) {
					prime = false;
				}
			}
			if (prime) {
				primes[primeInx++] = i;
			}
			i++;
		}
 
		return primes;
	}
 
	public static void main(String[] args) {
		new TimeExec(new Runnable() {
			public void run() {
				int[] primes = getPrimes(1000);
			}
		}, "Get 1,000 primes", System.out).start();
 
		//the 10,000 primes took the library's lab comp 19.125s
		new TimeExec(new Runnable() {
			public void run() {
				int[] primes = getPrimes(10000);
			}
		}, "Get 10,000 primes", System.out).start();
 
		new TimeExec(new Runnable() {
			public void run() {
				int[] primes = getPrimes(100000);
			}
		}, "Get 100,000 primes", System.out).start();
 
//		new TimeExec(new Runnable() {
//			public void run() {
//				int[] primes = getPrimes(1000000);
//			}
//		}, "Get 1,000,000 primes", System.out).start();
	}
}

---

I need to get it to be able to print out the 1,000,000 primes fairly quickly. Any help would be awesome, thank you!

There must be algorithms that google could find. Try that.

Try using a sieve. These are more memory intensive but they're very fast at finding prime numbers less than x.

For something fairly simple see Wikipedia: Sieve of Eratosthenese.

A little bit of self-promotion, but for moderately heavy prime generation (basically an optimized Sieve of Eratosthenes with a small hand-coded wheel factorization), see Optimizing the Sieve of Eratosthenes.

And for your balls-out bonkers version, see Prime Sieve, which I think is the current record holder for consecutive prime number generation. From what I can tell it's a multi-threaded Sieve of Eratosthenes with advanced wheel factorization. Unfortunately it's implemented in C++, not Java.

Sieves work great for finding lists of primes up to n, much faster than the method you are currently using (for a list of primes to 1000000, sieving returns the list in 64ms on my machine, while brute force returns it in 643 ms). However, I can give you some pointers if you want with your currents algorithm:

Code java:

---

for (int j = 2; j < i; j++) {
 
				if (i == i / j * j) {
					prime = false;
				}
			}

---

First, you upper bound is way to high. j need only go to the square root of i to check all possible factors. Also

Code java:

---

if (i == i / j * j) {
					prime = false;
				}

---

can be changed to

Code java:

---

if (i % j == 0) {
					prime = false;
				}

---

That percent sign thingy is called a modulo. What it does is it, in this case, divides i by j and returns the remainder. So, for example, 7 % 2 = 1 because when you long divide, you get 3 remainder 1 or simply 3 and 1/2. If i evenly divides into j, then it will always be zero, if not, then it will be some integer > 0.

One other thing with building the list your way, using the ArrayList class will be much, much easier than using that array.