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 . "\n" ); } } // Driver code $n = 15; primesInRange( $n ); // This code is contributed by mits ?> |
Output :
2 3 5 7 11 13
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