Given an integer N. The task is to find the next prime number i.e. the smallest prime number greater than N.
Examples:
Input: N = 10
Output: 11
11 is the smallest prime number greater than 10.Input: N = 0
Output: 2
Approach:
- First of all, take a boolean variable found and initialize it to false.
- Now, until that variable not equals to true, increment N by 1 in each iteration and check whether it is prime or not.
- If it is prime then print it and change value of found variable to True. otherwise, iterate the loop until you will get the next prime number.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
// Function that returns true if n // is prime else returns false bool isPrime( int n)
{ // Corner cases
if (n <= 1) return false ;
if (n <= 3) return true ;
// This is checked so that we can skip
// middle five numbers in below loop
if (n%2 == 0 || n%3 == 0) return false ;
for ( int i=5; i*i<=n; i=i+6)
if (n%i == 0 || n%(i+2) == 0)
return false ;
return true ;
} // Function to return the smallest // prime number greater than N int nextPrime( int N)
{ // Base case
if (N <= 1)
return 2;
int prime = N;
bool found = false ;
// Loop continuously until isPrime returns
// true for a number greater than n
while (!found) {
prime++;
if (isPrime(prime))
found = true ;
}
return prime;
} // Driver code int main()
{ int N = 3;
cout << nextPrime(N);
return 0;
} |
Java
// Java implementation of the approach class GFG
{ // Function that returns true if n
// is prime else returns false
static boolean isPrime( int n)
{
// Corner cases
if (n <= 1 ) return false ;
if (n <= 3 ) return true ;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0 ) return false ;
for ( int i = 5 ; i * i <= n; i = i + 6 )
if (n % i == 0 || n % (i + 2 ) == 0 )
return false ;
return true ;
}
// Function to return the smallest
// prime number greater than N
static int nextPrime( int N)
{
// Base case
if (N <= 1 )
return 2 ;
int prime = N;
boolean found = false ;
// Loop continuously until isPrime returns
// true for a number greater than n
while (!found)
{
prime++;
if (isPrime(prime))
found = true ;
}
return prime;
}
// Driver code
public static void main (String[] args)
{
int N = 3 ;
System.out.println(nextPrime(N));
}
} // This code is contributed by AnkitRai01 |
Python3
# Python3 implementation of the approach import math
# Function that returns True if n # is prime else returns False def isPrime(n):
# Corner cases
if (n < = 1 ):
return False
if (n < = 3 ):
return True
# This is checked so that we can skip
# middle five numbers in below loop
if (n % 2 = = 0 or n % 3 = = 0 ):
return False
for i in range ( 5 , int (math.sqrt(n) + 1 ), 6 ):
if (n % i = = 0 or n % (i + 2 ) = = 0 ):
return False
return True
# Function to return the smallest # prime number greater than N def nextPrime(N):
# Base case
if (N < = 1 ):
return 2
prime = N
found = False
# Loop continuously until isPrime returns
# True for a number greater than n
while ( not found):
prime = prime + 1
if (isPrime(prime) = = True ):
found = True
return prime
# Driver code N = 3
print (nextPrime(N))
# This code is contributed by Sanjit_Prasad |
C#
// C# implementation of the approach using System;
class GFG
{ // Function that returns true if n
// is prime else returns false
static bool isPrime( int n)
{
// Corner cases
if (n <= 1) return false ;
if (n <= 3) return true ;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false ;
for ( int i = 5; i * i <= n; i = i + 6)
if (n % i == 0 ||
n % (i + 2) == 0)
return false ;
return true ;
}
// Function to return the smallest
// prime number greater than N
static int nextPrime( int N)
{
// Base case
if (N <= 1)
return 2;
int prime = N;
bool found = false ;
// Loop continuously until isPrime
// returns true for a number
// greater than n
while (!found)
{
prime++;
if (isPrime(prime))
found = true ;
}
return prime;
}
// Driver code
public static void Main (String[] args)
{
int N = 3;
Console.WriteLine(nextPrime(N));
}
} // This code is contributed by 29AjayKumar |
Javascript
<script> // Javascript implementation of the approach // Function that returns true if n // is prime else returns false function isPrime(n)
{ // Corner cases
if (n <= 1) return false ;
if (n <= 3) return true ;
// This is checked so that we can skip
// middle five numbers in below loop
if (n%2 == 0 || n%3 == 0) return false ;
for (let i=5; i*i<=n; i=i+6)
if (n%i == 0 || n%(i+2) == 0)
return false ;
return true ;
} // Function to return the smallest // prime number greater than N function nextPrime(N)
{ // Base case
if (N <= 1)
return 2;
let prime = N;
let found = false ;
// Loop continuously until isPrime returns
// true for a number greater than n
while (!found) {
prime++;
if (isPrime(prime))
found = true ;
}
return prime;
} // Driver code let N = 3;
document.write(nextPrime(N));
// This code is contributed by Mayank Tyagi </script> |
Output:
5