Program to find Prime Numbers Between given Interval Last Updated : 11 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Given two numbers m and n as interval range, the task is to find the prime numbers in between this interval.Examples: Input: m = 1, n = 10Output: 2 3 5 7Input : m = 10, n = 20Output : 11 13 17 19Table of Content[Naive Approach] Basic Trial Division Method - O(n*n) Time and O(1) Space[Optimised Approach] Trial Division Method - O(n*sqrt(n)) Time and O(1) Space[Expected Approach] Using Sieve of Eratosthenes Method - O(nloglogn) Time and O(n) Space[Naive Approach] Basic Trial Division Method - O(n*n) Time and O(1) SpaceThe simplest method to check if a number i is prime by checking every number from 2 to i-1. If the number n is divisible by any of these, it's not prime. C++ // C++ program to find the prime numbers // between a given interval #include <bits/stdc++.h> using namespace std; bool isPrime(int n) { if (n <= 1) return false; for (int i = 2; i < n; i++) { if (n % i == 0) return false; } return true; } // Function to find all prime numbers in the range [m, n] vector<int> primeRange(int m, int n) { // Initialize a vector to store prime numbers vector<int> ans; // Iterate over each number in the range [m, n] for (int i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) ans.push_back(i); } return ans; } int main() { int m = 1, n = 10; vector<int> ans = primeRange(m, n); for (auto &i : ans) cout << i << " "; return 0; } Java // Java program to find the prime numbers // between a given interval class GfG { // Function to check if a number is prime static boolean isPrime(int n) { if (n <= 1) return false; for (int i = 2; i < n; i++) { if (n % i == 0) return false; } return true; } // Function to find all prime numbers in the range [m, // n] static int[] primeRange(int m, int n) { // Temporary array to store prime numbers int[] temp = new int[n - m + 1]; int index = 0; // Iterate over each number in the range [m, n] for (int i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) temp[index++] = i; } // Copy the prime numbers into a result array of // correct size int[] result = new int[index]; System.arraycopy(temp, 0, result, 0, index); return result; } public static void main(String[] args) { int m = 1, n = 10; int[] ans = primeRange(m, n); for (int i : ans) System.out.print(i + " "); } } Python # Python program to find the prime numbers # between a given interval # Function to check if a number is prime def isPrime(n): if n <= 1: return False for i in range(2, n): if n % i == 0: return False return True # Function to find all prime numbers in # the range [m, n] def primeRange(m, n): # Initialize a list to store prime numbers ans = [] # Iterate over each number in the range [m, n] for i in range(m, n + 1): # Check if the current number is prime if isPrime(i): ans.append(i) return ans if __name__ == "__main__": m, n = 1, 10 ans = primeRange(m, n) print(" ".join(map(str, ans))) C# // C# program to find the prime numbers // between a given interval using System; class GfG { // Function to check if a number is prime static bool isPrime(int n) { if (n <= 1) return false; for (int i = 2; i < n; i++) { if (n % i == 0) return false; } return true; } // Function to find all prime numbers in the range [m, // n] static int[] primeRange(int m, int n) { // Temporary array to store prime numbers int[] temp = new int[n - m + 1]; int index = 0; // Iterate over each number in the range [m, n] for (int i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) temp[index++] = i; } // Create result array of correct size int[] result = new int[index]; Array.Copy(temp, result, index); return result; } static void Main(string[] args) { int m = 1, n = 10; int[] ans = primeRange(m, n); foreach(int i in ans) Console.Write(i + " "); } } Javascript // JavaScript program to find the prime numbers // between a given interval // Function to check if a number is prime function isPrime(n) { if (n <= 1) return false; for (let i = 2; i < n; i++) { if (n % i === 0) return false; } return true; } // Function to find all prime numbers in the range [m, n] function primeRange(m, n) { // Initialize an array to store prime numbers let ans = []; // Iterate over each number in the range [m, n] for (let i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) ans.push(i); } return ans; } let m = 1, n = 10; let ans = primeRange(m, n); console.log(ans.join(" ")); Output2 3 5 7 [Optimised Approach] Trial Division Method - O(n*sqrt(n)) Time and O(1) SpaceThe idea is similar to previous approach but we check if a number if prime or not in sqrt(i) time because we just check for factors from number 2 to sqrt(i). For more details Please refer to Check for Prime Number. C++ // C++ program to find the prime numbers // between a given interval #include <bits/stdc++.h> using namespace std; bool isPrime(int n) { if (n <= 1) return false; if (n == 2) return true; // Numbers divisible by 2 are not prime if (n % 2 == 0) return false; for (int i = 3; i * i <= n; i += 2) { // If n is divisible by any odd number // in this range, it is not a prime number if (n % i == 0) return false; } return true; } // Function to find all prime numbers in the range [m, n] vector<int> primeRange(int m, int n) { vector<int> ans; for (int i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) ans.push_back(i); } return ans; } int main() { int m = 1, n = 10; vector<int> ans = primeRange(m, n); for (auto &i : ans) cout << i << " "; return 0; } Java // Java program to find the prime numbers // between a given interval class GfG { // Function to check if a number is prime static boolean isPrime(int n) { if (n <= 1) return false; if (n == 2) return true; // Numbers divisible by 2 are not prime if (n % 2 == 0) return false; for (int i = 3; i * i <= n; i += 2) { // If n is divisible by any odd number // in this range, it is not a prime number if (n % i == 0) return false; } return true; } // Function to find all prime numbers in the range [m, // n] static int[] primeRange(int m, int n) { // Temporary array to store prime numbers int[] temp = new int[n - m + 1]; int index = 0; // Iterate over each number in the range [m, n] for (int i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) { temp[index++] = i; } } // Create result array with the exact size int[] result = new int[index]; System.arraycopy(temp, 0, result, 0, index); return result; } public static void main(String[] args) { int m = 1, n = 10; int[] ans = primeRange(m, n); for (int num : ans) { System.out.print(num + " "); } } } Python # Python program to find the prime numbers # between a given interval # Function to check if a number is prime def isPrime(n): if n <= 1: return False if n == 2: return True # Numbers divisible by 2 are not prime if n % 2 == 0: return False # Check for factors from 3 to sqrt(n) for i in range(3, int(n**0.5) + 1, 2): if n % i == 0: return False return True # Function to find all prime numbers in the range [m, n] def primeRange(m, n): ans = [] # Iterate over each number in the range [m, n] for i in range(m, n + 1): # Check if the current number is prime if isPrime(i): ans.append(i) return ans if __name__ == "__main__": m, n = 1, 10 ans = primeRange(m, n) print(" ".join(map(str, ans))) C# // C# program to find the prime numbers // between a given interval using System; using System.Collections.Generic; class GfG { // Function to check if a number is prime static bool isPrime(int n) { if (n <= 1) return false; if (n == 2) return true; // Numbers divisible by 2 are not prime if (n % 2 == 0) return false; for (int i = 3; i * i <= n; i += 2) { if (n % i == 0) return false; } return true; } static int[] primeRange(int m, int n) { // Temporary array to store prime numbers int[] temp = new int[n - m + 1]; int index = 0; // Iterate over each number in the range [m, n] for (int i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) temp[index++] = i; } // Create result array of correct size int[] result = new int[index]; Array.Copy(temp, result, index); return result; } static void Main(string[] args) { int m = 1, n = 10; int[] ans = primeRange(m, n); foreach(int i in ans) Console.Write(i + " "); } } Javascript // JavaScript program to find the prime numbers // between a given interval // Function to check if a number is prime function isPrime(n) { if (n <= 1) return false; if (n === 2) return true; if (n % 2 === 0) return false; for (let i = 3; i * i <= n; i += 2) { if (n % i === 0) return false; } return true; } // Function to find all prime numbers in the range [m, n] function primeRange(m, n) { const ans = []; for (let i = m; i <= n; i++) { // Check if the current number is prime if (isPrime(i)) ans.push(i); } return ans; } // driver code const m = 1, n = 10; const ans = primeRange(m, n); console.log(ans.join(" ")); Output2 3 5 7 [Expected Approach] Using Sieve of Eratosthenes Method - O(nloglogn) Time and O(n) SpaceTo find all prime numbers in a given range [m, n], first implement the Sieve of Eratosthenes Method to mark non-prime numbers up to n. Create a boolean array prime[0..n] and initialize all entries as true, then mark prime[0] and prime[1] as false, since 0 and 1 are not prime numbers. Starting from p = 2, for each number p, mark all multiples of p greater than or equal to p*p as false (composite). After this step, all numbers marked as true are prime. Finally, iterate through the range [m, n] and collect all numbers that are still marked as true, which are the prime numbers between m and n. C++ // C++ program to find the prime numbers // between a given interval #include <bits/stdc++.h> using namespace std; // Function to implement the // Sieve of Eratosthenes to find primes up to 'n' vector<bool> sieveOfEratosthenes(int n) { // Create a boolean array "prime[0..n]" // and initialize all entries as true. // A value in prime[i] will be false // if 'i' is not prime, otherwise true. vector<bool> prime(n + 1, true); // Mark 0 and 1 as non-prime prime[0] = false; prime[1] = false; // Loop through numbers from 2 to sqrt(n) // to mark their multiples as non-prime for (int p = 2; p * p <= n; p++) { // If prime[p] is still true, it means 'p' is prime if (prime[p] == true) { // Mark all multiples of p greater // than or equal to p^2 as non-prime // Numbers less than p^2 would // have already been marked as non-prime for (int i = p * p; i <= n; i += p) prime[i] = false; } } return prime; } // Function to find all prime numbers in the range [m, n] vector<int> primeRange(int m, int n) { // Get the boolean array representing prime // numbers up to n vector<bool> isPrime = sieveOfEratosthenes(n); vector<int> ans; for (int i = m; i <= n; i++) { // If 'i' is prime, add it to the result list if (isPrime[i]) ans.push_back(i); } return ans; } int main() { int m = 1, n = 10; vector<int> ans = primeRange(m, n); for (auto &i : ans) cout << i << " "; return 0; } Java // Java program to find the prime numbers // between a given interval import java.util.*; class GfG { // Function to implement the // Sieve of Eratosthenes to find primes up to 'n' static boolean[] sieveOfEratosthenes(int n) { // Create a boolean array "prime[0..n]" // and initialize all entries as true. // A value in prime[i] will be false // if 'i' is not prime, otherwise true. boolean[] prime = new boolean[n + 1]; Arrays.fill(prime, true); // Mark 0 and 1 as non-prime prime[0] = false; prime[1] = false; // Loop through numbers from 2 to sqrt(n) // to mark their multiples as non-prime for (int p = 2; p * p <= n; p++) { // If prime[p] is still true, it means 'p' is // prime if (prime[p]) { // Mark all multiples of p greater // than or equal to p^2 as non-prime // Numbers less than p^2 would // have already been marked as non-prime for (int i = p * p; i <= n; i += p) prime[i] = false; } } return prime; } static int[] primeRange(int m, int n) { // Get the boolean array representing prime numbers // up to n boolean[] isPrime = sieveOfEratosthenes(n); // Count the number of primes in the range [m, n] int count = 0; for (int i = m; i <= n; i++) { if (isPrime[i]) count++; } // Create an array to store the prime numbers int[] ans = new int[count]; int index = 0; // Loop through the range [m, n] and collect all // prime numbers for (int i = m; i <= n; i++) { if (isPrime[i]) { ans[index++] = i; } } return ans; } public static void main(String[] args) { int m = 1, n = 10; int[] ans = primeRange(m, n); for (int i : ans) System.out.print(i + " "); } } Python # Python program to find the prime numbers # between a given interval # Function to implement the # Sieve of Eratosthenes to find primes up to 'n' def sieveOfEratosthenes(n): # Create a boolean array "prime[0..n]" # and initialize all entries as true. # A value in prime[i] will be false # if 'i' is not prime, otherwise true. prime = [True] * (n + 1) # Mark 0 and 1 as non-prime prime[0] = False prime[1] = False # Loop through numbers from 2 to sqrt(n) # to mark their multiples as non-prime for p in range(2, int(n**0.5) + 1): # If prime[p] is still true, it means 'p' is prime if prime[p] == True: # Mark all multiples of p greater # than or equal to p^2 as non-prime # Numbers less than p^2 would # have already been marked as non-prime for i in range(p * p, n + 1, p): prime[i] = False return prime # Function to find all prime numbers in the range [m, n] def primeRange(m, n): # Get the boolean array representing prime # numbers up to n isPrime = sieveOfEratosthenes(n) ans = [] # Loop through the range [m, n] and collect # all prime numbers for i in range(m, n + 1): # If 'i' is prime, add it to the result list if isPrime[i]: ans.append(i) return ans m, n = 1, 10 ans = primeRange(m, n) for i in ans: print(i, end=" ") C# // C# program to find the prime numbers // between a given interval using System; class GfG { // Function to implement the // Sieve of Eratosthenes to find primes up to 'n' static bool[] sieveOfEratosthenes(int n) { // Create a boolean array "prime[0..n]" // and initialize all entries as true. // A value in prime[i] will be false // if 'i' is not prime, otherwise true. bool[] prime = new bool[n + 1]; for (int i = 0; i <= n; i++) prime[i] = true; // Mark 0 and 1 as non-prime prime[0] = false; prime[1] = false; // Loop through numbers from 2 to sqrt(n) // to mark their multiples as non-prime for (int p = 2; p * p <= n; p++) { // If prime[p] is still true, it means 'p' is // prime if (prime[p]) { // Mark all multiples of p greater // than or equal to p^2 as non-prime // Numbers less than p^2 would // have already been marked as non-prime for (int i = p * p; i <= n; i += p) prime[i] = false; } } return prime; } // Function to find all prime numbers in the range [m, // n] static int[] primeRange(int m, int n) { // Get the boolean array representing prime numbers // up to n bool[] isPrime = sieveOfEratosthenes(n); // Count the number of primes in the range [m, n] int count = 0; for (int i = m; i <= n; i++) { if (isPrime[i]) count++; } // Create an array to store the prime numbers int[] ans = new int[count]; int index = 0; // Loop through the range [m, n] and collect all // prime numbers for (int i = m; i <= n; i++) { if (isPrime[i]) { ans[index++] = i; } } return ans; } static void Main() { int m = 1, n = 10; int[] ans = primeRange(m, n); foreach(int i in ans) Console.Write(i + " "); } } Javascript // JavaScript program to find the prime numbers // between a given interval // Function to implement the // Sieve of Eratosthenes to find primes up to 'n' function sieveOfEratosthenes(n) { // Create a boolean array "prime[0..n]" // and initialize all entries as true. // A value in prime[i] will be false // if 'i' is not prime, otherwise true. let prime = new Array(n + 1).fill(true); // Mark 0 and 1 as non-prime prime[0] = false; prime[1] = false; // Loop through numbers from 2 to sqrt(n) // to mark their multiples as non-prime for (let p = 2; p * p <= n; p++) { // If prime[p] is still true, it means 'p' is prime if (prime[p] === true) { // Mark all multiples of p greater // than or equal to p^2 as non-prime // Numbers less than p^2 would // have already been marked as non-prime for (let i = p * p; i <= n; i += p) prime[i] = false; } } return prime; } // Function to find all prime numbers in // the range [m, n] function primeRange(m, n) { // Get the boolean array representing prime numbers up // to n let isPrime = sieveOfEratosthenes(n); let ans = []; // Loop through the range [m, n] and collect all prime // numbers for (let i = m; i <= n; i++) { // If 'i' is prime, add it to the result list if (isPrime[i]) ans.push(i); } return ans; } let m = 1, n = 10; let ans = primeRange(m, n); console.log(ans.join(" ")); Output2 3 5 7 Comment More infoAdvertise with us Next Article Analysis of Algorithms R RishabhPrabhu Follow Improve Article Tags : Mathematical C Programs DSA Technical Scripter 2018 Prime Number school-programming +2 More Practice Tags : MathematicalPrime Number Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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