# Python Program to Check Prime Number

• Difficulty Level : Easy
• Last Updated : 30 Nov, 2018

Given a positive integer, check if the number is prime or not. A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of first few prime numbers are {2, 3, 5,

Examples:

```Input:  n = 11
Output: true

Input:  n = 15
Output: false

Input:  n = 1
Output: false
```

School Method :

 `# A school method based Python3 ``# program to check if a number``# is prime`` ` `def` `isPrime(n):`` ` `    ``# Corner case``    ``if` `n <``=` `1``:``        ``return` `False`` ` `    ``# Check from 2 to n-1``    ``for` `i ``in` `range``(``2``, n):``        ``if` `n ``%` `i ``=``=` `0``:``            ``return` `False``;`` ` `    ``return` `True`` ` `# Driver Program to test above function``print``(``"true"``) ``if` `isPrime(``11``) ``else` `print``(``"false"``)``print``(``"true"``) ``if` `isPrime(``14``) ``else` `print``(``"false"``)`` ` `# This code is contributed by Smitha Dinesh Semwal`

Output:

```true
false
```

Time complexity of this solution is O(n)

Optimized School Method :

 `# 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
```

Please refer complete article on Primality Test | Set 1 (Introduction and School Method) for more details!

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