Instructions

Test suite

Solution

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.

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. A good first test is to check that you do not use division or remainder operations (div, /, mod or % depending on the language).

To run the tests, run the command `dotnet test`

from within the exercise directory.

Initially, only the first test will be enabled. This is to encourage you to solve the exercise one step at a time.
Once you get the first test passing, remove the `Skip`

property from the next test and work on getting that test passing.
Once none of the tests are skipped and they are all passing, you can submit your solution
using `exercism submit Sieve.cs`

For more detailed information about the C# track, including how to get help if you're having trouble, please visit the exercism.io C# language page.

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

```
// This file was auto-generated based on version 1.1.0 of the canonical data.
using System;
using Xunit;
public class SieveTest
{
[Fact]
public void No_primes_under_two()
{
Assert.Throws<ArgumentOutOfRangeException>(() => Sieve.Primes(1));
}
[Fact(Skip = "Remove to run test")]
public void Find_first_prime()
{
var expected = new[] { 2 };
Assert.Equal(expected, Sieve.Primes(2));
}
[Fact(Skip = "Remove to run test")]
public void Find_primes_up_to_10()
{
var expected = new[] { 2, 3, 5, 7 };
Assert.Equal(expected, Sieve.Primes(10));
}
[Fact(Skip = "Remove to run test")]
public void Limit_is_prime()
{
var expected = new[] { 2, 3, 5, 7, 11, 13 };
Assert.Equal(expected, Sieve.Primes(13));
}
[Fact(Skip = "Remove to run test")]
public void Find_primes_up_to_1000()
{
var expected = new[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 };
Assert.Equal(expected, Sieve.Primes(1000));
}
}
```

```
using System;
using System.Linq;
public static class Sieve
{
public static int[] Primes(int limit)
{
if(limit < 2) throw new ArgumentOutOfRangeException();
var multiples = new int[] {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
var numberList = Enumerable.Range(2, limit-1).ToList();
foreach(int multiple in multiples.Where(x => x <= limit))
{
for(int i = 2; i <= limit / multiple; i++)
{
numberList.Remove(i * multiple);
}
}
return numberList.ToArray();
}
}
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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## Community comments

Interesting idea to start with a list of prime multiples. What is the maximum limit that this solution will work for? It seems that the first unique multiple of 37 (which is the first prime left off the multiples list) would fail to be removed. Did it pass all the tests?

I know the note says not to comment with any advice, so feel free to ignore.. but I wonder if you could replace the foreach loop with a for loop that runs through all the values in numberList & use that value in place of "multiple" in the next for loop. Then you wouldn't need the multiples array at all.