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

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 <bits/stdc++.h>` `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<n;k++){` ` ` `fact = fact * (k - ` `1` `);` ` ` `if` `((fact + ` `1` `) % k == ` `0` `)` ` ` `System.out.println(k);` ` ` `}` `}` `// Driver code` `public` `static` `void` `main(String[] args){` `int` `n = ` `15` `;` `primesInRange(n);` `}` `}` `// This code is contributed by mits` |

## 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<n;k++){` ` ` `fact = fact * (k - 1);` ` ` `if` `((fact + 1) % k == 0)` ` ` `System.Console.WriteLine(k);` ` ` `}` `}` `// Driver code` `static` `void` `Main(){` `int` `n = 15;` `primesInRange(n);` `}` `}` `// This code is contributed by mits` |

## PHP

`<?php` `// PHP program to prints prime numbers smaller than n` `function` `primesInRange(` `$n` `)` `{` ` ` `// Compute factorials and apply Wilson's` ` ` `// theorem.` ` ` `$fact` `= 1;` ` ` `for` `(` `$k` `=2;` `$k` `<` `$n` `;` `$k` `++){` ` ` `$fact` `= ` `$fact` `* (` `$k` `- 1);` ` ` `if` `((` `$fact` `+ 1) % ` `$k` `== 0)` ` ` `print` `(` `$k` `.` `"\n"` `);` ` ` `}` `}` `// Driver code` `$n` `= 15;` `primesInRange(` `$n` `);` `// This code is contributed by mits` `?>` |

## Javascript

`<script>` `// Javascript program to prints prime numbers smaller than n` `function` `primesInRange(n)` `{` ` ` `// Compute factorials and apply Wilson's` ` ` `// theorem.` ` ` `let fact = 1;` ` ` `for` `(let k = 2; k < n; k++){` ` ` `fact = fact * (k - 1);` ` ` `if` `((fact + 1) % k == 0)` ` ` `document.write((k + ` `"<br>"` `));` ` ` `}` `}` `// Driver code` `let n = 15;` `primesInRange(n);` `// This code is contributed by _saurabh_jaiswal` `</script>` |

**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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