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Find the sum of all the prime numbers

A friend of mine who is learning to program in C, was having diffculty in writing a program to find the sum of all the prime numbers between a specified limit (in her case 3-60). I helped her out with the program, and I thought I'll post it here which might help others.

Code: C

`/* ** Program to find the sum of all numbers between 3 and 60 ** @author : Pradeep ** @date : 11/29/2006 */  #include <stdio.h>  void main(void) {     unsigned int i,j,s=0,is_prime;      for(i=3;i<=60;i++)     {         is_prime = 1; // Assuming that current value of i is prime                  // Checking for prime         for(j=2;j<=(i/2);j++)         {             if(i%j==0) // Not prime, set is_prime to 0 and break             {                 is_prime = 0;                 break;             }         }          if(is_prime) // If the number is prime, sum it up         {             s += i;             // optionally you can print the prime numbers too             printf("%d ",i);         }     }      printf("\n\nThe sum of the prime numbers = %d",s); }`

 friendsforniraj 29Nov2006 15:06

Re: Find the sum of all the prime numbers

well this code is good but it ll take more time(for computational work)
please check this code the 2nd for loop

Code:

``` /* ** Program to find the sum of all numbers between 3 and 60 ** @author : Pradeep ** @date : 11/29/2006 */  #include <stdio.h>  #include<math.h> void main(void)   {     printf("\n please enter the upper limit");   int n;     scanf("%d",&n);\\now n can be given by user     unsigned int i,j,s=0,is_prime;        for(i=3;i<=n;i++)     {        is_prime = 1; // Assuming that current value of i is prime                // Checking for prime          for(j=2;j<=sqrt(i);j++)        {            if(i%j==0) // Not prime, set is_prime to 0 and break            {             is_prime = 0;                      break;                }        }        if(is_prime) // If the number is prime, sum it up          {  s += i;            // optionally you can print the prime numbers too             printf("%d ",i);        }    }    printf("\n\nThe sum of the prime numbers = %d",s);  }```
//see though your program will work proper but if we have to sum up prime nos. between 3 to n
//where n verey big(though within the limits of int :-) )
// then the checkin condition from to n/2 will take lot of time
// suppose ur n==100 then it will check from n=2 to n=50
//so the no. of checking loops required for 100 will be 48
//where as if we go from n=2 to n= 10 we only require 8 loops so it will be much faster
// now think for the case of n=1000 wouldnt it will take lot of time

Re: Find the sum of all the prime numbers

I understood your point, but I see you have used sqrt() ! How does that help?? And we need to check whether it got a factor execpt for itself and 1 or not.

 shabbir 29Nov2006 15:36

Re: Find the sum of all the prime numbers

I would use
t = sqrt(i);
in
for(j=2;j<=sqrt(i);j++)
e.g.
for(j=2;j<=t;j++)
So it does not need to calc square root all the time it loops through j

 friendsforniraj 29Nov2006 15:41

Re: Find the sum of all the prime numbers

yes i got you!
the thing is we dont need to go more than the sqrt of the no. which to be checked as prime if it is not divisibe by any no. upto sqrt(n) than there wont be any factor above that you can check it for any no.

Re: Find the sum of all the prime numbers

Its not using square root anywhere, and neither does it require too. Could you please tell me why does it need to use square root??

 friendsforniraj 29Nov2006 15:46

Re: Find the sum of all the prime numbers

good point shabbir

 shabbir 29Nov2006 16:17

Re: Find the sum of all the prime numbers

Quote:
 Originally Posted by pradeep Its not using square root anywhere, and neither does it require too. Could you please tell me why does it need to use square root??
He edited the code to find a no is prime or not to loop till the sqrt(n) and not till n/2

Re: Find the sum of all the prime numbers

For example, sqrt(60) = 7.46, that means we will loop 7 times, but 60 is divisible by 30 also.
The program works fine with sqrt, but what is the logic?

 shabbir 29Nov2006 18:00

Re: Find the sum of all the prime numbers

But 30 is the largets no. The smallest you will find is less than the sqrt(n).

For logic refer http://en.wikipedia.org/wiki/Prime_number Finding prime numbers section

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