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
// Java Program to Generate Prime// Numbers Between Given Rangeclass 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)
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
// Java Program to Implement // Sieve of eratosthenes// to Generate Prime Numbers // Between Given Rangeimport 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))
.png)