Java Algorithms How to - Compute prime numbers

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Question

We would like to know how to compute prime numbers.

Answer

/* Compute prime numbers, after Knuth, Vol 1, Sec 1.3.2, Alg. "P".
 * Unlike Knuth, I don't build table formatting into
 * computational programs; output is one per line.
 * <p>/*from   w  w  w  . j  ava  2s  .  c  om*/
 * Note that there may be more efficient algorithms for finding primes.
 * Consult a good book on numerical algorithms.
 * @author Ian Darwin
 */
public class Main {
  /** 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 = 100;

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

    long stop = DEFAULT_STOP;
    stop = 100;

    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]);
  }
}

The code above generates the following result.

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