public class PrimeSieve {
public static void main(String[] args) {
int N = Integer.parseInt(args[0]);
// initially assume all integers are prime
boolean[] isPrime = new boolean[N + 1];
for (int i = 2; i <= N; i++) {
isPrime[i] = true;
}
// mark non-primes <= N using Sieve of Eratosthenes
for (int i = 2; i*i <= N; i++) {
// if i is prime, then mark multiples of i as nonprime
// suffices to consider mutiples i, i+1, ..., N/i
if (isPrime[i]) {
for (int j = i; i*j <= N; j++) {
isPrime[i*j] = false;
}
}
}
// count primes
int primes = 0;
for (int i = 2; i <= N; i++) {
if (isPrime[i]) primes++;
}
System.out.println("The number of primes <= " + N + " is " + primes);
}
}
/*************************************************************************
* Computes the number of primes less than or equal to N using
* the Sieve of Eratosthenes.
*
* % java PrimeSieve 25
* The number of primes <= 25 is 9
*
* % java PrimeSieve 100
* The number of primes <= 100 is 25
*
* % java -Xmx100m PrimeSieve 100000000
* The number of primes <= 100000000 is 5761455
*
* % java PrimeSieve -Xmx1100m 1000000000
* The number of primes <= 1000000000 is 50847534
*
*
* The 110MB and 1100MB is the amount of memory you want to allocate
* to the program. If your computer has less, make this number smaller,
* but it may prevent you from solving the problem for very large
* values of N.
*
*
* N Primes <= N
* ---------------------------------
* 10 4
* 100 25
* 1,000 168
* 10,000 1,229
* 100,000 9,592
* 1,000,000 78,498
* 10,000,000 664,579
* 100,000,000 5,761,455
* 1,000,000,000 50,847,534
*
*************************************************************************/
Not Satisfied ? Just search & get the result
Related posts:
