Python program to check whether a number is Prime or not

Last Updated: 05-09-2020

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):                  # 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:

1. 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.
2. 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