Java Examples in a Nutshell, 3rd Edition

Computing Primes

Example 1-15 computes the largest prime number less than a specified value, using the Sieve of Eratosthenes algorithm. The algorithm finds primes by eliminating multiples of all lower prime numbers. Like Example 1-14, this example introduces no new Java syntax, but is a nice, nontrivial program with which to end this chapter. The program may seem deceptively simple, but there’s actually a fair bit going on, so be sure you understand how it is ruling out prime numbers.

Example 1-15. Sieve.java

package je3.basics;

/**
 * This program computes prime numbers using the Sieve of Eratosthenes
 * algorithm: rule out multiples of all lower prime numbers, and anything
 * remaining is a prime.  It prints out the largest prime number less than
 * or equal to the supplied command-line argument.
 **/
public class Sieve {
    public static void main(String[  ] args) {
        // We will compute all primes less than the value specified on the
        // command line, or, if no argument, all primes less than 100.
        int max = 100;                           // Assign a default value
        try { max = Integer.parseInt(args[0]); } // Parse user-supplied arg
        catch (Exception e) {  }                   // Silently ignore exceptions.

        // Create an array that specifies whether each number is prime or not.
        boolean[  ] isprime = new boolean[max+1];

        // Assume that all numbers are primes, until proven otherwise.
        for(int i = 0; i <= max; i++) isprime[i] = true;

        // However, we know that 0 and 1 are not primes.  Make a note of it.
        isprime[0] = isprime[1] = false;

        // To compute all primes less than max, we need to rule out
        // multiples of all integers less than the square root of max.
        int n = (int) Math.ceil(Math.sqrt(max));  // See java.lang.Math class

        // Now, for each integer i from 0 to n:
        //   If i is a prime, then none of its multiples are primes,
        //   so indicate this in the array.  If i is not a prime, then
        //   its multiples have already been ruled out by one of the
        //   prime factors of i, so we can skip this case.
        for(int i = 0; i <= n; i++) {
            if (isprime[i])                          // If i is a prime, 
                for(int j = 2*i; j <= max; j = j + i) // loop through multiples
                    isprime[j] = false;               // they are not prime.
        }

        // Now go look for the largest prime:
        int largest;
        for(largest = max; !isprime[largest]; largest--) ;  // empty loop body
        
        // Output the result
        System.out.println("The largest prime less than or equal to " + max +
                           " is " + largest);
    }
}