This Java program shows a simple method of computing prime numbers with Java.

Java Code:
public class Primes {
  /** The default stopping point for primes */
  public static final long DEFAULT_STOP = 4294967295L;
  /** The first prime number */
  public static final int FP = 2;

  static int MAX = 10000;

  public static void main(String[] args) {
    long[] prime = new long[MAX];

    long stop = DEFAULT_STOP;
    if (args.length == 1) {
      stop = Long.parseLong(args[0]);
    }

    prime[1] = FP;       // P1 (ignore prime[0])
    long n = FP+1;       // odd candidates
    int j = 1;        // numberFound

    boolean isPrime = true;  // for 3

    do {

      if (isPrime) {
        if (j == MAX-1) {
          // Grow array dynamically if needed
          long[] np = new long[MAX * 2];
          System.arraycopy(prime, 0, np, 0, MAX);
          MAX *= 2;
          prime = np;
        }
        prime[++j] = n;  // P2
        isPrime = false;
      }
      n += 2;        // P4

      for (int k = 2; k <= j && k < MAX; k++) {  // P5, P6, P8
        long q = n / prime[k];
        long r = n % prime[k];
        if (r == 0) {      
          break;
        }
        if (q <= prime[k]) {    // P7
          isPrime = true;
          break;
        }
      }
    } while (n < stop);        // P3

    for (int i=1; i<=j; i++)
      System.out.println(prime[i]);
  }
}