Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Python program to check whether a number is Prime or not

  • Difficulty Level : Easy
  • Last Updated : 10 Nov, 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 : 

 Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.  

To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. And to begin with your Machine Learning Journey, join the Machine Learning - Basic Level Course

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: 

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")
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.

Now lets see the code for the first optimization method ( i.e. checking till √n )

Python3




from math import sqrt
# n is the number to be check whether it is prime or not
n = 1
  
# no lets check from 2 to sqrt(n)
# if we found any facto then we can print as not a prime number
  
# this flag maintains status whether the n is prime or not
prime_flag = 0
  
if(n > 1):
    for i in range(2, int(sqrt(n)) + 1):
        if (n % i == 0):
            prime_flag = 1
            break
    if (prime_flag == 0):
        print("true")
    else:
        print("false")
else:
    print("false")
Output
false

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)




My Personal Notes arrow_drop_up
Recommended Articles
Page :