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# Number which is co-prime with all integers from a given range

• Last Updated : 31 May, 2021

Given two positive integers L and R, the task is to find an integer X greater than 1 such that X is co-prime with all the integers from the range [L, R].

Examples:

Input: L = 16, R = 17
Output: 19
Explanation: Only number which is co-prime with all the integers from the range [16, 17] is 9.

Input: L = 973360, R = 973432
Output: 973439

Approach: The simplest approach to solve the given problem is to find a prime number greater than R, because this integer does not divide any integer in the range of [L, R]. Therefore, the idea is to iterate from the value (R + 1) and if there exists any integer which is prime, then print that integer and break out of the loop.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach #include using namespace std; // Function to check whether the// given number N is prime or notbool isPrime(int N){    // Base Case    if (N == 1)        return false;     for (int i = 2; i * i <= N; i++) {         // If N has more than one        // factor, then return false        if (N % i == 0)            return false;    }     // Otherwise, return true    return true;} // Function to find X which is co-prime// with the integers from the range [L, R]int findCoPrime(int L, int R){    // Store the resultant number    int coPrime;     // Check for prime integers    // greater than R    for (int i = R + 1;; i++) {         // If the current number is        // prime, then update coPrime        // and break out of loop        if (isPrime(i)) {            coPrime = i;            break;        }    }     // Print the resultant number    return coPrime;} // Driver Codeint main(){    int L = 16, R = 17;    cout << findCoPrime(L, R);     return 0;}

## Java

 // Java program for the above approachimport java.io.*;import java.lang.*;import java.util.*; class GFG{ // Function to check whether the// given number N is prime or notstatic boolean isPrime(int N){         // Base Case    if (N == 1)        return false;     for(int i = 2; i * i <= N; i++)    {                 // If N has more than one        // factor, then return false        if (N % i == 0)            return false;    }     // Otherwise, return true    return true;} // Function to find X which is co-prime// with the integers from the range [L, R]static int findCoPrime(int L, int R){         // Store the resultant number    int coPrime;     // Check for prime integers    // greater than R    for(int i = R + 1;; i++)    {                 // If the current number is        // prime, then update coPrime        // and break out of loop        if (isPrime(i))        {            coPrime = i;            break;        }    }     // Print the resultant number    return coPrime;} // Driver Codepublic static void main(String[] args){    int L = 16, R = 17;         System.out.println(findCoPrime(L, R));}} // This code is contributed by Kingash

## Python3

 # Python3 program for the above approach # Function to check whether the# given number N is prime or notdef isPrime(N):    # Base Case    if (N == 1):        return False     for i in range(2, N + 1):        if i*i > N:            break                     # If N has more than one        # factor, then return false        if (N % i == 0):            return False     # Otherwise, return true    return True # Function to find X which is co-prime# with the integers from the range [L, R]def findCoPrime(L, R):       # Store the resultant number    coPrime, i = 0, R + 1     # Check for prime integers    # greater than R    while True:         # If the current number is        # prime, then update coPrime        # and break out of loop        if (isPrime(i)):            coPrime = i            break        i += 1     # Print the resultant number    return coPrime # Driver Codeif __name__ == '__main__':    L,R = 16, 17    print (findCoPrime(L, R)) # This code is contributed by mohit kumar 29.

## C#

 // C# program for the above approachusing System; class GFG{ // Function to check whether the// given number N is prime or notstatic bool isPrime(int N){         // Base Case    if (N == 1)        return false;     for(int i = 2; i * i <= N; i++)    {                 // If N has more than one        // factor, then return false        if (N % i == 0)            return false;    }     // Otherwise, return true    return true;} // Function to find X which is co-prime// with the integers from the range [L, R]static int findCoPrime(int L, int R){     // Store the resultant number    int coPrime;     // Check for prime integers    // greater than R    for(int i = R + 1;; i++)    {                 // If the current number is        // prime, then update coPrime        // and break out of loop        if (isPrime(i))        {            coPrime = i;            break;        }    }     // Print the resultant number    return coPrime;} // Driver Codepublic static void Main(string[] args){    int L = 16, R = 17;     Console.WriteLine(findCoPrime(L, R));}} // This code is contributed by ukasp

## Javascript


Output:
19

Time Complexity: O(L * R1/2)
Auxiliary Space: O(1)

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