Java Program to Implement Sieve of Eratosthenes to Generate Prime Numbers Between Given Range
A number which is divisible by 1 and itself or a number which has factors as 1 and the number itself is called a prime number. The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million or so.
Example:
Input : from = 1, to = 20 Output: 2 3 5 7 11 13 17 19 Input : from = 4, to = 15 Output: 5 7 11 13
A. Naive approach:
- Define a function named isprime(int n) which will check if a number is prime or not.
- Run a loop from "from" to "to".
- Inside for loop, check if i is prime, then print the value of i
Below is the implementation of the above approach:
// Java Program to Generate Prime
// Numbers Between Given Range
class GFG {
public static boolean isprime(int n)
{
if (n == 1)
return false;
for (int i = 2; i <= Math.sqrt(n); i++)
// Check if a number has factors
// its not prime and return 0
if (n % i == 0)
return false;
// Check if a number dont
// have any factore
// its prime and return 1
return true;
}
public static void main(String[] args)
{
// Suppose we want to print
// prime no. from 1 to 20
int from = 1, to = 20, k = 0;
for (int i = from; i <= to; i++)
if (isprime(i))
System.out.print(" " + i);
}
}
Output
2 3 5 7 11 13 17 19
Time complexity: O(n3/2)
Auxiliary space: O(1) as it is using constant space for variables
B. Sieve of Eratosthenes:
Initially, assume every number from 0 to n is prime, assign array value of each number as 1. After that, strike off each non-prime number by changing the value from 1 to 0 in an array and finally, print only those numbers whose array value is 1, i.e. prime numbers.
Approach:
- Input n from user
- In array, fill 1 corresponding to each element
- Do a[0]=0 and a[1]=0 as we know 0,1 are not prime
- Assume 1st number(2) to be prime and strike off the multiples of 2(as the multiples of 2 will be non-prime)
- Continue step 3 till square root(n)
- Print the list containing non-striked (or prime) numbers.
Below is the implementation of the above approach:
// Java Program to Implement
// Sieve of eratosthenes
// to Generate Prime Numbers
// Between Given Range
import java.util.*;
class GFG {
public static void main(String[] args)
{
int from = 1, to = 20, i;
boolean[] a = new boolean[to + 1];
Arrays.fill(a, true);
// 0 and 1 are not prime
a[0] = false;
a[1] = false;
for (i = 2; i <= Math.sqrt(to); i++)
// Check if number is prime
if (a[i])
for (int j = i * i; j <= to; j += i) {
a[j] = false;
}
for (i = from; i <= to; i++) {
// Printing only prime numbers
if (a[i])
System.out.print(" " + i);
}
}
}
Output
2 3 5 7 11 13 17 19
Time Complexity: O(n log(log n))
Auxiliary Space: O(n)