A Sieve Method for Prime Numbers

 1 #include <stdio.h>
 2 #define MAX 1000
 3 #define SAVE 0
 4 #define DELETE 1
 5 
 6 int sieve[1000]={0}; //all to SAVE
 7 
 8 int main()
 9 {
10     int i,k;
11     int prime;
12     int count=1;//The sum number of the prime numbers 
13     //2*i+3 is odd numbers
14     for(i=0;i<MAX;i++)
15     {
16         if(sieve[i]==SAVE) //it is a prime number 
17         {
18             //I have a problem here.Why are the front several numbers prime number after one or two sieve process such as 5 or 7 or 11? I just think they are prime nubmers without proving it.  
19             prime=i+i+3; 
20             count++;
21             for(k=prime+i;k<=MAX;k+=prime)
22                 sieve[k]=DELETE;
23         }
24     }
25     printf("%6d",2);
26 
27     for(i=0,k=2;i<MAX;i++)
28     {
29         if(sieve[i]==SAVE)
30         {
31             if(k>10) 
32             {
33                 printf("\n"); 
34                 k=1;
35             }
36             int temp=i+i+3;
37             printf("%6d",temp);
38             k++;
39         }
40     }
41     printf("\nThe sum number is %d \n",count);
42     return 0;
43 }