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Python program to check whether a number is Prime or not
• Difficulty Level : Easy
• Last Updated : 24 Feb, 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 :

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:

## C

 `// C program for``// the above approach``#include ``int` `main()``{``    ``// Given number``    ``int` `n = 11;``    ``// checking the given number``    ``// whether it is 1 or not``    ``if` `(n == 1) {``        ``printf``(``"%d is not a prime number"``, n);``    ``}``    ``else` `{``        ``int` `f = 0;``        ``// iterate from 2 to n/2``        ``for` `(``int` `i = 2; i <= (n / 2); i++) {``          ` `            ``// If n is divisible by any number between``            ``// 2 and n/2, it is not prime``            ``if` `(n % 2 == 0) {``                ``f = 1;``              ` `                ``// break out of for loop as``                ``// it is not prime``                ``break``;``            ``}``        ``}``        ``if` `(f == 1) {``            ``printf``(``"%d is not a prime number"``, n);``        ``}``        ``else` `{``            ``printf``(``"%d is a prime number"``, n);``        ``}``    ``}``    ``return` `0;``}``// This Code is Contributed by``// Murarishetty Santhosh Charan`

## 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"``)`

## C++

 `// C++ program for``// the above approach``#include ``using` `namespace` `std;` `int` `main() {``    ``// Given number``    ``int` `n=11;``    ``// checking the given number``    ``// whether it is 1 or not``      ``if``(n==1)``      ``{``          ``cout<
Output
`11 is a prime number`

Optimized Method
We can do the following optimizations:

1. 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.
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)

## Python3

 `# 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.`

Output:

``` true
false```

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