Sieve of Erathostenes

Sieve of Erathosthenes
In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. It works efficiently for the smaller primes (below 10 million) . It was created by Eratosthenes, an ancient Greek mathematician.
The Algorithm
1. Create a contiguous list of numbers from two to some highest number n.
2. Strike out from the list all multiples of two (4, 6, 8 etc.).
3. The list's next number that has not been struck out is a prime number.
4. Strike out from the list all multiples of the number you identified in the previous step.
5. Repeat steps 3 and 4 until you reach a number that is greater than the square root of n (the highest number in the list).
6. All the remaining numbers in the list are prime.

Output

25 Primes to 100
    2    3    5    7   11
   13   17   19   23   29
   31   37   41   43   47
   53   59   61   67   71
   73   79   83   89   97

Twin Primes
3       5
5       7
11      13
17      19
29      31
41      43
59      61
71      73
Press any key to continue . . .

The code

//
// Sieve of Erathosthenes
//
#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

int main ()
{
   const int TO = 100;
   int sieve[TO + 1];   // Just ignore sieve[0]
   int index;
   int count;
  
   //
   // first fill the sieve
   //
   for(index=0; index < TO + 1; index++) sieve[index]=index;
  
   //
   // start marking out non primes
   // start at 2
   for(index=2; index <= sqrt(TO); index++) {
      if(! sieve[index]) continue;   // already marked out
      for(int inner=index+index; inner < TO + 1; inner+=index)
         sieve[inner]=0; // mark out all multiples of index
   }
   //
   // count the primes
   //
   count=0;
   for(index=2; index < TO +1; index++)
    if(sieve[index]) count++;
   //
   // print the primes
   //
   cout << count << " Primes to " << TO << endl;
   count=0;
   for(index=2; index < TO +1; index++)
      if(sieve[index]) {
        cout << setw (5) << sieve[index];
        if(!(++count % 5)) cout << endl;
      }
   //
   // print the twin primes
   //
   cout << endl <<  "Twin Primes " << endl;
   for(index=2; index< TO; index++)
     if(sieve[index] && sieve[index+2])
      cout << sieve[index] << "\t" 
           << sieve[index+2] << endl;
         
   system("pause");
   return 0;
}