# 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<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 ` |

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## 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 ` |

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## 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) ` |

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## 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 ` |

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## 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 ` `?> ` |

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**Output :**

2 3 5 7 11 13

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

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