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Sync the sieve exercise's docs with the latest data. (#321)
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66 changes: 40 additions & 26 deletions exercises/practice/sieve/.docs/instructions.md
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# Instructions

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.

[This wikipedia article][eratosthenes] has a useful graphic that explains the algorithm.

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).

[eratosthenes]: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find all prime numbers less than or equal to a given number.

A prime number is a number larger than 1 that is only divisible by 1 and itself.
For example, 2, 3, 5, 7, 11, and 13 are prime numbers.
By contrast, 6 is _not_ a prime number as it not only divisible by 1 and itself, but also by 2 and 3.

To use the Sieve of Eratosthenes, you first create a list of all the numbers between 2 and your given number.
Then you repeat the following steps:

1. Find the next unmarked number in your list (skipping over marked numbers).
This is a prime number.
2. Mark all the multiples of that prime number as **not** prime.

You keep repeating these steps until you've gone through every number in your list.
At the end, all the unmarked numbers are prime.

~~~~exercism/note
The tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.
To check you are implementing the Sieve correctly, a good first test is to check that you do not use division or remainder operations.
~~~~

## Example

Let's say you're finding the primes less than or equal to 10.

- List out 2, 3, 4, 5, 6, 7, 8, 9, 10, leaving them all unmarked.
- 2 is unmarked and is therefore a prime.
Mark 4, 6, 8 and 10 as "not prime".
- 3 is unmarked and is therefore a prime.
Mark 6 and 9 as not prime _(marking 6 is optional - as it's already been marked)_.
- 4 is marked as "not prime", so we skip over it.
- 5 is unmarked and is therefore a prime.
Mark 10 as not prime _(optional - as it's already been marked)_.
- 6 is marked as "not prime", so we skip over it.
- 7 is unmarked and is therefore a prime.
- 8 is marked as "not prime", so we skip over it.
- 9 is marked as "not prime", so we skip over it.
- 10 is marked as "not prime", so we stop as there are no more numbers to check.

You've examined all numbers and found 2, 3, 5, and 7 are still unmarked, which means they're the primes less than or equal to 10.
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# Introduction

You bought a big box of random computer parts at a garage sale.
You've started putting the parts together to build custom computers.

You want to test the performance of different combinations of parts, and decide to create your own benchmarking program to see how your computers compare.
You choose the famous "Sieve of Eratosthenes" algorithm, an ancient algorithm, but one that should push your computers to the limits.

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