Where is the Sieve of Eratosthenes used today?

Question

I'm doing a research paper on the topic and while I find a lot of examples and discussion about how the algorithm works/should be implemented, I can't find anything on where it's actually used.

Is there any field in which the algorithm is used today? Or do people just implement it for "shits 'n giggles" (it's fairly simple, so that would make some sense)?

I know that large prime numbers are important in the field of encryption, but I doubt the sieve is used to find/generate those primes. Also, the huge amount of memory needed to find large primes makes it inefficient for those, too.

So is the algorithm, in any form, used anywhere today?

Answer 1

According to the Wikipedia article on the subject, that particular sieve is still a very efficient method for producing the full list of primes whose value is less than a few millions. Also, the general idea of a sieve is used in several other, more powerful algorithms, such as the General number field sieve for factoring large integers.

Answer 2

You can view a prime sieve as an application of dynamic programming to small complete prime number enumeration and testing. So your question is really "what do we need prime numbers for?". They are a fundamental part of number theory. As one example encoding an integer into its prime factorization has all sorts of useful properties and higher-level utility. By adding backtracking to a sieve we can perform this factorization very quickly.