Syntax error An interesting solution to get all prime numbers smaller than n?

An interesting solution to get all prime numbers smaller than n?

Here we will see how to generate all prime numbers that are less than n in an efficient way. In this approach we will use the Wilson’s theorem. According to his theorem if a number k is prime, then ((k - 1)! + 1) mod k will be 0. Let us see the algorithm to get this idea.

This idea will not work in C or C++ like language directly, because it will not support the large integers. The factorial will generate large numbers.

Algorithm

genAllPrime(n)

Begin
   fact := 1
   for i in range 2 to n-1, do
      fact := fact * (i - 1)
      if (fact + 1) mod i is 0, then
         print i
      end if
   done
End

Example

#include <iostream>
using namespace std;
void genAllPrimes(int n){
   int fact = 1;
   for(int i=2;i<n;i++){
      fact = fact * (i - 1);
      if ((fact + 1) % i == 0){
         cout<< i << " ";
      }
   }
}
int main() {
   int n = 10;
   genAllPrimes(n);
}

Output

2 3 5 7
Updated on: 2020-07-02T09:40:59+05:30

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