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An interesting solution to get all prime numbers smaller than n

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

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


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