The prime numbers are used to calculate the sum of positive divisors of any positive integer.
Dear Jaber, it depends on the size, in bits, of the prime numbers you're wanting to search, however you should take a look at the GMP library wich has a prime iterator, and the GSL library wich also has as similar tool. However in all cases, a more complex library, poorly documented, exists called FLINT, it's based on the GMP library and uses advanced techniques such as the Field Sieve to check if the number is prime or not.
Yes, SAGE is also a great option. It even includes Pari-GP inside it, but it is a lot more heavier (in size) and quite more complex to learn than Pari (although the result may be worth the effort!) . In SAGE you can do any kind of mathematical manipulation, from linear algebra to number theory to differential calculus to combinatorial algebra.
I would recommend investing in Mathematica. It is an ideal platform for all kinds of mathematics, including very efficient functions for prime number theory. I have used it for more than 10 years now and have never been disappointed. Most of all, because Mathematica has so many built-in highly optimized functions, you can focus the majority of your time on the actual problem that you started out with - instead of worrying about writing programs from scratch. Just my 5 cents from a lot of experience.
On the smaller scale, I made several program to compute prime, prime factor and positive divisors. You can check from my tutorial in http://people.revoledu.com/kardi/tutorial/BasicMath/Prime/index.html. Hoping that helps
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