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eratosthenes prime test exercise
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# Sieve
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Use the Sieve of Eratosthenes to find all the primes from 2 up to a given
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number.
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The Sieve of Eratosthenes is a simple, ancient algorithm for finding all
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prime numbers up to any given limit. It does so by iteratively marking as
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composite (i.e. not prime) the multiples of each prime, starting with the
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multiples of 2. It does not use any division or remainder operation.
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Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])
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The algorithm consists of repeating the following over and over:
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- take the next available unmarked number in your list (it is prime)
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- mark all the multiples of that number (they are not prime)
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Repeat until you have processed each number in your range.
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When the algorithm terminates, all the numbers in the list that have not
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been marked are prime.
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The wikipedia article has a useful graphic that explains the algorithm:
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https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
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Notice that this is a very specific algorithm, and the tests don't check
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that you've implemented the algorithm, only that you've come up with the
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correct list of primes. A good first test is to check that you do not use
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division or remainder operations (div, /, mod or % depending on the
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language).
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## Exception messages
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Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to
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indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not
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every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include
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a message.
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To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
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`raise Exception`, you should write:
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```python
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raise Exception("Meaningful message indicating the source of the error")
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```
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## Running the tests
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To run the tests, run the appropriate command below ([why they are different](https://github.com/pytest-dev/pytest/issues/1629#issue-161422224)):
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- Python 2.7: `py.test sieve_test.py`
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- Python 3.4+: `pytest sieve_test.py`
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Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
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`python -m pytest sieve_test.py`
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### Common `pytest` options
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- `-v` : enable verbose output
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- `-x` : stop running tests on first failure
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- `--ff` : run failures from previous test before running other test cases
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For other options, see `python -m pytest -h`
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## Submitting Exercises
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Note that, when trying to submit an exercise, make sure the solution is in the `$EXERCISM_WORKSPACE/python/sieve` directory.
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You can find your Exercism workspace by running `exercism debug` and looking for the line that starts with `Workspace`.
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For more detailed information about running tests, code style and linting,
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please see [Running the Tests](http://exercism.io/tracks/python/tests).
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## Source
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Sieve of Eratosthenes at Wikipedia [http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes](http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
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## Submitting Incomplete Solutions
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It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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