# Sieve

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given
number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all
prime numbers up to any given limit. It does so by iteratively marking as
composite (i.e. not prime) the multiples of each prime,
starting with the multiples of 2.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

- take the next available unmarked number in your list (it is prime)
- mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not
been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm:
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check
that you've implemented the algorithm, only that you've come up with the
correct list of primes.

## Rust Installation

Refer to the [exercism help page][help-page] for Rust installation and learning
resources.

## Writing the Code

Execute the tests with:

```bash
$ cargo test
```

All but the first test have been ignored.  After you get the first test to
pass, remove the ignore flag (`#[ignore]`) from the next test and get the tests
to pass again.  The test file is located in the `tests` directory.   You can
also remove the ignore flag from all the tests to get them to run all at once
if you wish.

Make sure to read the [Modules](https://doc.rust-lang.org/book/second-edition/ch07-00-modules.html) chapter if you
haven't already, it will help you with organizing your files.

## Feedback, Issues, Pull Requests

The [exercism/rust](https://github.com/exercism/rust) repository on GitHub is the home for all of the Rust exercises. If you have feedback about an exercise, or want to help implement new exercises, head over there and create an issue. Members of the [rust track team](https://github.com/orgs/exercism/teams/rust) are happy to help!

If you want to know more about Exercism, take a look at the [contribution guide](https://github.com/exercism/docs/blob/master/contributing-to-language-tracks/README.md).

[help-page]: http://exercism.io/languages/rust
[modules]: https://doc.rust-lang.org/book/second-edition/ch07-00-modules.html
[cargo]: https://doc.rust-lang.org/book/second-edition/ch14-00-more-about-cargo.html

## Source

Sieve of Eratosthenes at Wikipedia [http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes](http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)

## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.