# 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.

## Getting Started

Make sure you have read [the C++ page](http://exercism.io/languages/cpp) on
exercism.io.  This covers the basic information on setting up the development
environment expected by the exercises.

## Passing the Tests

Get the first test compiling, linking and passing by following the [three
rules of test-driven development](http://butunclebob.com/ArticleS.UncleBob.TheThreeRulesOfTdd).
Create just enough structure by declaring namespaces, functions, classes,
etc., to satisfy any compiler errors and get the test to fail.  Then write
just enough code to get the test to pass.  Once you've done that,
uncomment the next test by moving the following line past the next test.

```C++
#if defined(EXERCISM_RUN_ALL_TESTS)
```

This may result in compile errors as new constructs may be invoked that
you haven't yet declared or defined.  Again, fix the compile errors minimally
to get a failing test, then change the code minimally to pass the test,
refactor your implementation for readability and expressiveness and then
go on to the next test.

Try to use standard C++11 facilities in preference to writing your own
low-level algorithms or facilities by hand.  [CppReference](http://en.cppreference.com/)
is a wiki reference to the C++ language and standard library.  If you
are new to C++, but have programmed in C, beware of
[C traps and pitfalls](http://www.slideshare.net/LegalizeAdulthood/c-traps-and-pitfalls-for-c-programmers).

## 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.