Python program to check whether a number is Prime or not

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:

# 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, num//2): 
         
       # 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 following optimizations:

Instead of checking till n, we can check till √n because a larger factor of n must be a multiple of 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)

# 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. 

Main Article : Primality Test | Set 1 (Introduction and School Method)

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