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)