Abstract. This article describes the calculation of prime numbers with the sieve of Eratosthenes in Java
1. Prime Factorization
A prime is an integer greater than one whole only positive divisors are one and itself.
The prime counting function for a number N (also known as pie(N)) is the number of primes less or equal to N. The following algorithm determines all prime numbers until a certain value.
2. Implementation in Java
Create a Java project "de.vogella.algorithms.primenumbers".
Create the following program.
package de.vogella.algorithms.primenumbers;
import java.util.ArrayList;
import java.util.List;
// Using the sieve of Eratosthenes
public class PrimeNumbers {
public static List<Integer> calcPrimeNumbers(int n) {
boolean[] isPrimeNumber = new boolean[n + 1]; // boolean defaults to
// false
List<Integer> primes = new ArrayList<Integer>();
for (int i = 2; i < n; i++) {
isPrimeNumber[i] = true;
}
for (int i = 2; i < n; i++) {
if (isPrimeNumber[i]) {
primes.add(i);
// now mark the multiple of i as non-prime number
for (int j = i; j * i <= n; j++) {
isPrimeNumber[i * j] = false;
}
}
}
return primes;
}
public static void main(String[] args) {
List<Integer> calcPrimeNumbers = calcPrimeNumbers(21);
for (Integer integer : calcPrimeNumbers) {
System.out.println(integer);
}
System.out.println("Prime counting function (Pie(N)) : "
+ calcPrimeNumbers.size());
}
}3. Links and Literature
Nothing listed.
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