# Sieve

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).