I have been practicing coding tests again. One nice exercise I saw the other day was a sample from a HackerRank test: find the number of prime numbers less than N. Or tell how many primes are below a given limit. You can easily change the problem to pick the list of the said primes.

It is such a classic problem that I decided to dedicate myself to write a nice solution, because I couldn’t find a really good “functional style” implementation in Scala, strictly with immutable collections, and using `foldLeft` if possible. And there is also an important detail about this problem that is worth talking about. The most well known solution is not actually the “best” one, and the difference isn’t even that that big. So it really is a subject we should all be studying a little bit more carefully.

This article discusses four different solutions to the problem. First is the most usual solution, the so-called *unfaithful sieve.* Then we will show the most “cult” solution to this problem, the sieve of Eratosthenes. These both can be written recursively, but the first can actually be implemented with a fold. We will then show a quite different implementation of the sieve, using a map to store known composite numbers, that I came up with myself, even though I doubt is new. We finish by looking at implementations of the two algorithms using mutable collections.