# 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): ` `        `  `       ``# 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)
3.  `# 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)

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : kumarakhilakak