# PrimeSieve.java

Below is the syntax highlighted version of PrimeSieve.java from §1.4 Arrays.

```/******************************************************************************
*  Compilation:  javac PrimeSieve.java
*  Execution:    java -Xmx1100m PrimeSieve n
*
*  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
*
******************************************************************************/

public class PrimeSieve {
public static void main(String[] args) {
int n = Integer.parseInt(args);

// 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 factor = 2; factor*factor <= n; factor++) {

// if factor is prime, then mark multiples of factor as non-prime
// suffices to consider multiples factor, factor+1, ...,  n/factor
if (isPrime[factor]) {
for (int j = factor; factor*j <= n; j++) {
isPrime[factor*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);
}
}
```