# Python Program to Check Prime Number

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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