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 codeint main(){ int n = 15; primesInRange(n);}// This code is contributed by Rajput-Ji |
Java
// Java program prints prime numbers smaller than nclass 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 codepublic 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 ndef 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 coden = 15primesInRange(n) |
C#
// C# program prints prime numbers smaller than nclass 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 codestatic void Main(){int n = 15;primesInRange(n);}}// This code is contributed by mits |
PHP
<?php// PHP program to prints prime numbers smaller than nfunction 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 nfunction 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 codelet 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 neveropen and would like to contribute, you can also write an article using write.neveropen.co.za or mail your article to review-team@neveropen.co.za. See your article appearing on the neveropen 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.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
