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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

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." ");
            }
}
  
// Driver code
$n = 15;
primesInRange($n);
  
// This code is contributed by mits
?>


Output :

2
3
5
7
11
13

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



This article is attributed to GeeksforGeeks.org

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