Java Program to Implement Sieve of Eratosthenes to Generate Prime Numbers Between Given Range Last Updated : 12 Sep, 2022 Comments Improve Suggest changes Like Article Like Report 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 13A. 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 iBelow is the implementation of the above approach: Java // 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 19Time 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 userIn array, fill 1 corresponding to each elementDo a[0]=0 and a[1]=0 as we know 0,1 are not primeAssume 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 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) Comment More infoAdvertise with us Next Article Segmented Sieve P pradiptamukherjee Follow Improve Article Tags : Java Technical Scripter Java Programs Technical Scripter 2020 Practice Tags : Java Similar Reads Check for Prime Number Given a number n, check whether it is a prime number or not.Note: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.Input: n = 7Output: trueExplanation: 7 is a prime number because it is greater than 1 and has no divisors other than 1 and itself.Input: n 11 min read Primality Test AlgorithmsIntroduction to Primality Test and School MethodGiven a positive integer, check if the number is prime or not. 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But O(sqrt n) method times out when we need to answer multiple queries regarding prime factorization.In this article, we study an efficient method to calculate the prime factorization using O(n) space and O(log 11 min read Java Program to Implement Sieve of Eratosthenes to Generate Prime Numbers Between Given RangeA 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 Out 3 min read Segmented Sieve Given a number n, print all primes smaller than n. Input: N = 10Output: 2, 3, 5, 7Explanation : The output â2, 3, 5, 7â for input N = 10 represents the list of the prime numbers less than or equal to 10. Input: N = 5Output: 2, 3, 5 Explanation : The output â2, 3, 5â for input N = 5 represents the li 15+ min read Segmented Sieve (Print Primes in a Range) Given a range [low, high], print all primes in this range? For example, if the given range is [10, 20], then output is 11, 13, 17, 19. A Naive approach is to run a loop from low to high and check each number for primeness. A Better Approach is to precalculate primes up to the maximum limit using Sie 15 min read Longest sub-array of Prime Numbers using Segmented Sieve Given an array arr[] of N integers, the task is to find the longest subarray where all numbers in that subarray are prime. Examples: Input: arr[] = {3, 5, 2, 66, 7, 11, 8} Output: 3 Explanation: Maximum contiguous prime number sequence is {2, 3, 5} Input: arr[] = {1, 2, 11, 32, 8, 9} Output: 2 Expla 13 min read Sieve of Sundaram to print all primes smaller than n Given a number n, print all primes smaller than or equal to n.Examples: Input: n = 10Output: 2, 3, 5, 7Input: n = 20Output: 2, 3, 5, 7, 11, 13, 17, 19We have discussed Sieve of Eratosthenes algorithm for the above task. Below is Sieve of Sundaram algorithm.printPrimes(n)[Prints all prime numbers sma 10 min read Like