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# 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. It does not use any division or remainder operation.
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. A good first test is to check that you do not use
division or remainder operations (div, /, mod or % depending on the
language).
## 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, open the tests source file which is located in the `tests` directory
and remove the `#[ignore]` flag from the next test and get the tests to pass
again. Each separate test is a function with `#[test]` flag above it.
Continue, until you pass every test.
If you wish to run all ignored tests without editing the tests source file, use:
```bash
$ cargo test -- --ignored
```
To run a specific test, for example `some_test`, you can use:
```bash
$ cargo test some_test
```
If the specific test is ignored use:
```bash
$ cargo test some_test -- --ignored
```
To learn more about Rust tests refer to the [online test documentation][rust-tests]
Make sure to read the [Modules][modules] chapter if you
haven't already, it will help you with organizing your files.
## Further improvements
After you have solved the exercise, please consider using the additional utilities, described in the [installation guide](https://exercism.io/tracks/rust/installation), to further refine your final solution.
To format your solution, inside the solution directory use
```bash
cargo fmt
```
To see, if your solution contains some common ineffective use cases, inside the solution directory use
```bash
cargo clippy --all-targets
```
## Submitting the solution
Generally you should submit all files in which you implemented your solution (`src/lib.rs` in most cases). If you are using any external crates, please consider submitting the `Cargo.toml` file. This will make the review process faster and clearer.
## 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 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]: https://exercism.io/tracks/rust/learning
[modules]: https://doc.rust-lang.org/book/ch07-02-defining-modules-to-control-scope-and-privacy.html
[cargo]: https://doc.rust-lang.org/book/ch14-00-more-about-cargo.html
[rust-tests]: https://doc.rust-lang.org/book/ch11-02-running-tests.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.
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