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# Instructions | ||
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Use the Sieve of Eratosthenes to find all the primes from 2 up to a given | ||
number. | ||
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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. | ||
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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) | ||
- 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 | ||
been marked are prime. | ||
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[This wikipedia article][eratosthenes] has a useful graphic that explains the algorithm. | ||
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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). | ||
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[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. | ||
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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. | ||
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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 (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 | ||
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. | ||
~~~~ | ||
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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. |
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# Introduction | ||
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You bought a big box of random computer parts at a garage sale. | ||
You've started putting the parts together to build custom computers. | ||
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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. |