Finding prime numbers (Sieve of Eratosthenes): Range of Error --> where & how to fix?

Hi,

I had to write this program based on the algorithm given at the beginning of the program. This program has a range of error, but I still can't figure out where & how to fix it. Could you please help?

Code:

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// Exercise 13 (Ch.4)
// Based on the Sieve of Eratosthenes algorithm provided on www.wikipedia.org
/*
        1.        Create a list of consecutive integers from two to n: (2, 3, 4, ..., n).
        2.        Initially, let p equal 2, the first prime number.
        3.        Strike from the list all multiples of p greater than p.
        4.        Find the first number remaining on the list greater than p (this number is the next prime);
            Let p equal this number.
        5.        Repeat steps 3 and 4 until p2 is greater than n.
        6.        All the remaining numbers on the list are prime.

*/
#include "std_lib_facilities.h"

int square(int x)
{
        return x*x;
}
int main()
{
        vector<unsigned int>numbers;
        vector<unsigned int>primes;
        unsigned int n=100;
        unsigned int i, p;
       
        // Create a list of consecutive integers from 2 - n
        for(i=2; i<=n;++i)
                numbers.push_back(i);
       
        p=2; // First prime number
        primes[0]=p;
        while(square(p)<=n) {
               
                for(i=0;i<numbers.size();++i) {
                        if(numbers[i]>p && (numbers[i]%p)!=0)
                                primes.push_back(numbers[i]);
                }
                for(i=0;i<primes.size();++i) {
                        if(primes[i]>p) {
                                p=primes[i];
                                break;
                        }       
                }
       
        }
       
        for(i=0; i<primes.size();++i)
                cout<<primes[i]<<endl;
}

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because you are taking powers of p instead of taking multiples of p.

Check out the prime number contest in the contest forum, I believe one of the entries was a sieve implementation.

here is a quicky version -

Code:

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#include <stdio.h>

#define PMAX 100

unsigned int Seive[PMAX];

int main(){
        for(int i = 0;i<PMAX;i++) Seive[i] = i+2;

        unsigned int Index = 0;
        unsigned int p = 0;
        unsigned int temp = 0;

        while(Index < PMAX){
                p = Seive[Index];
                if(p == 0){
                        Index++;
                        continue;
                        }
                printf("%d\n" , p);
                temp = p + p;
                while(temp < (PMAX + 2)){
                        Seive[temp-2] = 0;
                        temp += p;
                        }
                Index++;
                }

        return 0;
        }

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Hint: How many items are there in the primes vector just before this line?:

Code:

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primes[0]=p;

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