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# Instructions | ||
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Your task is to create a program that implements the Sieve of Eratosthenes algorithm to find prime numbers. | ||
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. | ||
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A prime number is a number that is only divisible by 1 and itself. | ||
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. | ||
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The Sieve of Eratosthenes is an ancient algorithm that works by taking a list of numbers and crossing out all the numbers that aren't prime. | ||
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A number that is **not** prime is called a "composite number". | ||
By contrast, 6 is _not_ a prime number as it not only divisible by 1 and itself, but also by 2 and 3. | ||
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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: | ||
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1. Find the next unmarked number in your list. This is a prime number. | ||
2. Mark all the multiples of that prime number as composite (not prime). | ||
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. | ||
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You keep repeating these steps until you've gone through every number in your list. | ||
At the end, all the unmarked numbers are prime. | ||
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~~~~exercism/note | ||
[Wikipedia's Sieve of Eratosthenes article][eratosthenes] has a useful graphic that explains the algorithm. | ||
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. | ||
[eratosthenes]: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes | ||
To check you are implementing the Sieve correctly, a good first test is to check that you do not use division or remainder operations. | ||
~~~~ | ||
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## Example | ||
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Let's say you're finding the primes less than or equal to 10. | ||
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- 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. | ||
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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. |