`1` ```exercism fetch python sieve ```

# 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.

## Exception messages

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of `raise Exception`, you should write:

 `1` ```raise Exception("Meaningful message indicating the source of the error") ```

## Running the tests

To run the tests, run the appropriate command below (why they are different):

• Python 2.7: `py.test sieve_test.py`
• Python 3.3+: `pytest sieve_test.py`

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version): `python -m pytest sieve_test.py`

### Common `pytest` options

• `-v` : enable verbose output
• `-x` : stop running tests on first failure
• `--ff` : run failures from previous test before running other test cases

For other options, see `python -m pytest -h`

## Submitting Exercises

Note that, when trying to submit an exercise, make sure the solution is in the `\$EXERCISM_WORKSPACE/python/sieve` directory.

You can find your Exercism workspace by running `exercism debug` and looking for the line that starts with `Workspace`.

For more detailed information about running tests, code style and linting, please see the help page.

## Source

Sieve of Eratosthenes at Wikipedia 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.