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.

Answer 2

public class PrimeNumberGeneration {

public static void main(String[] args) {
    // TODO Auto-generated method stub

    Scanner scan = new Scanner(System.in);
    int n = scan.nextInt();

    ArrayList<Integer> primeNumbers = new ArrayList<Integer>();
    primeNumbers.add(2);
    System.out.println(2);

    no_loop:
    for(int no=3; no<=n; no+=2){
        for(Integer primeNumber: primeNumbers){
            if((no%primeNumber)==0){
                continue no_loop;
            }
        }
        primeNumbers.add(no);
        System.out.println(no);
    }

}

}

Answer 3

Here is my Soluction.

public class PrimeNumberGenerator {

public static void print(int n) {
    // since 1 is not prime number.
    for (int i = 2; i <= n; i++) {
        if (isPrime(i)) {
            System.out.print(i + "\n");
        }
    }

}

public static boolean isPrime(int num) {

    for (int i = 2; i * i <= num; i++) {
        if (num % i == 0) {
            return false;
        }
    }

    return true;
}

public static void main(String[] args) {
    print(10);
  }

}

Output: 2 3 5 7