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

• Difficulty Level : Easy
• Last Updated : 18 Aug, 2022

This approach is based on Wilson’s theorem and uses the fact that factorial computation can be done easily using DP
Wilson’s theorem says if a number k is prime then ((k-1)! + 1) % k must be 0.

Below is a 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 < n; k++) {``        ``fact = fact * (k - 1);``        ``if` `((fact + 1) % k == 0)``            ``cout << k << endl;``    ``}``}` `// Driver code``int` `main()``{``    ``int` `n = 15;``    ``primesInRange(n);``}``// This code is contributed by Rajput-Ji`

## 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)`

## 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

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## Javascript

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Output :

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

Time Complexity: O(n)

Auxiliary Space: O(1)

This article is contributed by Parikshit Mukherjee. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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