Python program to check whether a number is Prime or not

Difficulty Level : Easy
Last Updated : 24 Feb, 2021

Given a positive integer N, The task is to write a Python program to check if the number is prime or not.
Definition: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are {2, 3, 5, 7, 11, ….}.

Examples :

Input: n = 11
Output: true

Input: n = 15
Output: false

Input: n = 1
Output: false

The idea to solve this problem is to iterate through all the numbers starting from 2 to (N/2) using a for loop and for every number check if it divides N. If we find any number that divides, we return false. If we did not find any number between 2 and N/2 which divides N then it means that N is prime and we will return True.

Below is the Python program to check if a number is prime:

C

// C program for
// the above approach
#include <stdio.h>
int main()
{
    // Given number
    int n = 11;
    // checking the given number
    // whether it is 1 or not
    if (n == 1) {
        printf("%d is not a prime number", n);
    }
    else {
        int f = 0;
        // iterate from 2 to n/2
        for (int i = 2; i <= (n / 2); i++) {
           
            // If n is divisible by any number between
            // 2 and n/2, it is not prime
            if (n % 2 == 0) {
                f = 1;
               
                // break out of for loop as
                // it is not prime
                break;
            }
        }
        if (f == 1) {
            printf("%d is not a prime number", n);
        }
        else {
            printf("%d is a prime number", n);
        }
    }
    return 0;
}
// This Code is Contributed by
// Murarishetty Santhosh Charan

Python3

# Python program to check if
# given number is prime or not
 
num = 11
 
# If given number is greater than 1
if num > 1:
 
    # Iterate from 2 to n / 2
    for i in range(2, int(num/2)+1):
 
        # If num is divisible by any number between
        # 2 and n / 2, it is not prime
        if (num % i) == 0:
            print(num, "is not a prime number")
            break
    else:
        print(num, "is a prime number")
 
else:
    print(num, "is not a prime number")

C++

// C++ program for
// the above approach
#include <bits/stdc++.h>
using namespace std;
 
int main() {
    // Given number
    int n=11;
    // checking the given number 
    // whether it is 1 or not
      if(n==1)
      {
          cout<<n<<" is not a prime number";
      }
      else
      {
          int f=0;
          // iterate from 2 to n/2
          for(int i=2;i<=(n/2);i++)
          {
              // If n is divisible by any number between
            // 2 and n/2, it is not prime
              if(n%2==0)
              {
                  f=1;
                  // break out of for loop as 
                  // it is not prime
                  break;
              }
          }
          if(f==1)
          {
              cout<<n<<" is not a prime number";
          }
          else
          {
              cout<<n<<" is a prime number";
          }
      }
    return 0;
}
// This code is contributed by
// Murarishetty Santhosh Charan

Output

11 is a prime number

Optimized Method
We can do the following optimizations:

Instead of checking till n, we can check till √n because a larger factor of n must be a multiple of a smaller factor that has been already checked.
The algorithm can be improved further by observing that all primes are of the form 6k ± 1, with the exception of 2 and 3. This is because all integers can be expressed as (6k + i) for some integer k and for i = ?1, 0, 1, 2, 3, or 4; 2 divides (6k + 0), (6k + 2), (6k + 4); and 3 divides (6k + 3). So a more efficient method is to test if n is divisible by 2 or 3, then to check through all the numbers of form 6k ± 1. (Source: wikipedia)

Python3

# A optimized school method based 
# Python3 program to check 
# if a number is prime 
 
 
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
 
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
 
    return True
 
 
# Driver Program 
if (isPrime(11)) : 
    print(" true") 
else : 
    print(" false") 
     
if(isPrime(15)) : 
    print(" true") 
else : 
    print(" false") 
     
     
# This code is contributed 
# by Nikita Tiwari. 

Output:

 true
 false

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