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++
#include<bits/stdc++.h>
using namespace std;
void primesInRange(int n)
{
int fact = 1;
for(int k=2;k<n;k++){
fact = fact * (k - 1);
if ((fact + 1) % k == 0)
cout<<k<<endl;
}
}
int main()
{
int n = 15;
primesInRange(n);
}
|
Java
class GFG{
static void primesInRange(int n)
{
int fact = 1;
for(int k=2;k<n;k++){
fact = fact * (k - 1);
if ((fact + 1) % k == 0)
System.out.println(k);
}
}
public static void main(String[] args){
int n = 15;
primesInRange(n);
}
}
|
Python3
def primesInRange(n) :
fact = 1
for k in range(2, n):
fact = fact * (k - 1)
if ((fact + 1) % k == 0):
print k
n = 15
primesInRange(n)
|
C#
class GFG{
static void primesInRange(int n)
{
int fact = 1;
for(int k=2;k<n;k++){
fact = fact * (k - 1);
if ((fact + 1) % k == 0)
System.Console.WriteLine(k);
}
}
static void Main(){
int n = 15;
primesInRange(n);
}
}
|
PHP
<?php
function primesInRange($n)
{
$fact = 1;
for($k=2;$k<$n;$k++){
$fact = $fact * ($k - 1);
if (($fact + 1) % $k == 0)
print($k."\n");
}
}
$n = 15;
primesInRange($n);
?>
|
Javascript
<script>
function primesInRange(n)
{
let fact = 1;
for(let k = 2; k < n; k++){
fact = fact * (k - 1);
if ((fact + 1) % k == 0)
document.write((k + "<br>"));
}
}
let n = 15;
primesInRange(n);
</script>
|
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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