Prime Number Generator Logic

Question

I am supposed to make a class PrimeNumberGenerator which has a method nextPrime that will print out all prime numbers up to a number the user input

Answer 1

Doing primality check on each and every number is inefficient in your case. Use Sieve_of_Eratosthenes instead, to find all prime numbers up to any given limit.

public class PrimeGenerator {

  private final BitSet primes;

  private int nextPrime = 0;

  /**
   * Sieve of Eratosthenes
   */
  public PrimeGenerator(final int LIMIT)
  {
    primes = new BitSet(LIMIT+1);
    primes.set(2, LIMIT);

    for (int i = 4; i < LIMIT; i += 2)
      primes.clear(i);

    final int SQRT = (int) Math.sqrt(LIMIT);
    for (int p = 3; p <= SQRT; p = primes.nextSetBit(p+2)) {
      for (int j = p * p; j <= LIMIT; j += 2 * p) {
        primes.clear(j);
      }
    }
  }

  public int nextPrime()
  {
    nextPrime = primes.nextSetBit(nextPrime + 1);
    return nextPrime;
  }

  public static void main(String[] args) {
    // print primes up to 1000
    PrimeGenerator primeGen = new PrimeGenerator(50);
    int prime = primeGen.nextPrime();
    while (prime != -1) {
      System.out.println(prime);
      prime = primeGen.nextPrime();
    }
  }
}

Optimization tips when implementing Sieve of Eratosthenes:

• Iterate only over the odd numbers. Because all the multiples of 2, except for 2 is composite.

• Start eliminating from (p * p). So for instance for the prime number 3, you should start eliminating from 9.

• Increment by 2 * p instead of p, so to avoid even numbers.

This could generate millions of primes in just seconds.