# An interesting solution to get all prime numbers smaller than n

This approach is based on Wilson’s theorem and using the fact that factorial computation can be done easily using DP

Wilson theorem says if a number k is prime then ((k-1)! + 1) % k must be 0.

Below is Python implementation of the approach. Note that the solution works in Python because Python supports large integers by default therefore factorial of large numbers can be computed.

## C++

 `// C++ program to Prints prime numbers smaller than n ` `#include ` `using` `namespace` `std; ` `void` `primesInRange(``int` `n) ` `{ ` `    ``// Compute factorials and apply Wilson's  ` `    ``// theorem. ` `    ``int` `fact = 1; ` `    ``for``(``int` `k=2;k

## Java

 `// Java program prints prime numbers smaller than n ` `class` `GFG{ ` `static` `void` `primesInRange(``int` `n) ` `{ ` `    ``// Compute factorials and apply Wilson's  ` `    ``// theorem. ` `    ``int` `fact = ``1``; ` `    ``for``(``int` `k=``2``;k

## Python3

 `# Python3 program to prints prime numbers smaller than n ` `def` `primesInRange(n) : ` ` `  `    ``# Compute factorials and apply Wilson's  ` `    ``# theorem. ` `    ``fact ``=` `1` `    ``for` `k ``in` `range``(``2``, n): ` `        ``fact ``=` `fact ``*` `(k ``-` `1``) ` `        ``if` `((fact ``+` `1``) ``%` `k ``=``=` `0``): ` `            ``print` `k ` ` `  `# Driver code ` `n ``=` `15` `primesInRange(n) `

/div>

## C#

 `// C# program prints prime numbers smaller than n ` `class` `GFG{ ` `static` `void` `primesInRange(``int` `n) ` `{ ` `    ``// Compute factorials and apply Wilson's  ` `    ``// theorem. ` `    ``int` `fact = 1; ` `    ``for``(``int` `k=2;k

## PHP

 ` `

Output :

```2
3
5
7
11
13
```

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

This article is attributed to GeeksforGeeks.org

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