# 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).


Run the tests with:

```bash
bats sieve_test.sh
```

After the first test(s) pass, continue by commenting out or removing the
`[[ $BATS_RUN_SKIPPED == true ]] || skip` 
annotations prepending other tests.

To run all tests, including the ones with `skip` annotations, run:

```bash
BATS_RUN_SKIPPED=true bats sieve_test.sh
```

## Source

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


## External utilities
`Bash` is a language to write "scripts" -- programs that can call
external tools, such as
[`sed`](https://www.gnu.org/software/sed/),
[`awk`](https://www.gnu.org/software/gawk/),
[`date`](https://www.gnu.org/software/coreutils/manual/html_node/date-invocation.html)
and even programs written in other programming languages, 
like [`Python`](https://www.python.org/).
This track does not restrict the usage of these utilities, and as long
as your solution is portable between systems and does not require
installation of third party applications, feel free to use them to solve
the exercise.

For an extra challenge, if you would like to have a better understanding
of the language, try to re-implement the solution in pure `Bash`,
without using any external tools. Note that there are some types of
problems that bash cannot solve, such as performing floating point
arithmetic and manipulating dates: for those, you must call out to an
external tool.

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