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 360). I helped her out with the program, and I thought I'll post it here which might help others.
Code: C

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 */ //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.

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 
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??

Re: Find the sum of all the prime numbers
good point shabbir

Re: Find the sum of all the prime numbers
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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? 
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 
Re: Find the sum of all the prime numbers
There is other method also which does not require sqrt.
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Re: Find the sum of all the prime numbers
Interesting, so we will find the factor of n within any of the number in sqrt(n) if not then its a prime number.

Re: Find the sum of all the prime numbers
let me tell you the logic now
it is very simple look if k is any no. then k can be represented as k=i*j where i and are k's factor now i varies from 1to k and j varies from k to 1 but for prime no. we check for i=2 to k/2 acordingly j will varies from (k/2) to 2 now if 2 is a factor of k then automatically k/2 is also a factor and so on that is when i increases, j decreases so we continue like this then there is condition that both i and j becomes equal so i*i=k so i=sqrt(k) but if k is not a square of any no. then i increases upto a integer just less than sqrt iof k thats all what i did now try this problem for a given no. print all its prime factors that is if input is 12 out put should be 2*2*3 using the hint that the lowest factor of any no. other than one is always prime try it 
Re: Find the sum of all the prime numbers
friendsforniraj thats a good logic explained.

Re: Find the sum of all the prime numbers
thank u sir
but ma name is niraj 
Re: Find the sum of all the prime numbers
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Re: Find the sum of all the prime numbers
why do we need a square root

Re: Find the sum of all the prime numbers
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Re: Find the sum of all the prime numbers
for(j=2;j<=sqrt(i);j++) :cryin:
is similar to for(j=2;j*j <= i;j++) :p so, no sqrt in here since it is really slow. At least if was some years ago. 
Re: Find the sum of all the prime numbers
for getting the prime number try
http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes No devisions in here 
Re: Find the sum of all the prime numbers
Its wonderful how such an apparently trivial problem of finding prime numbers is turning into such an animated discussion on various algorithmic techniques  each with its own benefits & pitfalls!
Wikipedia's page on the prime number is as exhaustive as its page on human evolution! It just goes to show how fascinating Mathematics is that it throws a challenge in something as apparently simple as finding primes. It also demonstrates the importance of algorithmic design & analysis for effective computing  even the biggest supercomputer on the planet cannot achieve its true computational potential if the algorithm involves excessive looping or is inefficient! Also, a special thanks to Niraj (friendsofniraj), who has given an extremely succint explanation of how the Square Root logic works  there was no need for me to read a single word on Wiki about the algorithm (although I did to satiate my curiosity  and might I say, it is very thoroughly dissected in Wikipedia!) And also the keen eye of Shabbir noticed the redundancy in the calculation of Square Root through the innerloop! All in all  a very fascinating discussion! Regards, Rajiv 
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