C++ Program to Generate Prime Numbers Between a Given Range Using the Sieve of Sundaram

This is C++ program to implement Sieve of Sundaram to Generate Prime Numbers Between Given Range. This algorithm was discovered in 1934 by Sundaram.

Algorithm

Begin
   printPrimes(n)
   Here we find out primes
   smaller than n, we reduce n-2 to half. We call it New.
   New = (n-2)/2;
   Create an array marked[n] that is going
   to be used to separate numbers of the form i+j+2ij from
   others where 1 <= i <= j
   Initialize all entries of marked[] as false.
   Mark all numbers of the form i + j + 2ij as true
   where 1 <= i <= j
   for i=1 to New
      a) j = i;
      b) Loop While (i + j + 2*i*j) 2, then print 2 as first prime.
      Remaining primes are of the form 2i + 1 where i is
      index of NOT marked numbers. So print 2i + 1 for all i
      such that marked[i] is false.
End

Example Code

#include <bits/stdc++.h>
using namespace std;
int SieveOfSundaram(int m) {
   int N= (m-2)/2;
   bool marked[N + 1];
   memset(marked, false, sizeof(marked));
   for (int i=1; i<=N; i++)
      for (int j=i; (i + j + 2*i*j) <= N; j++)
         marked[i + j + 2*i*j] = true;
      if (m > 2)
         cout << 2 << " ";
   for (int i=1; i<=N; i++)
      if (marked[i] == false)
         cout << 2*i + 1 << " ";
}
int main(void) {
   int m = 10;
   SieveOfSundaram(m);
   return 0;
}

Output

2 3 5 7