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 in Python.

Examples: 

Input:  n = 11
Output: True


Input:  n = 1
Output: False

What is the Prime number

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, ….}. 

Prime Number Program in Python 

Method 1: 

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.

Python3

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

Method 2: Fastest Algorithm to Find Prime Numbers

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 let’s 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

# 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