Sync the sieve exercise's docs with the latest data.

Author: ErikSchierboom

exercises/practice/sieve/.docs/instructions.md

@@ -1,28 +1,42 @@
 # Instructions
 
-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.
 
-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.
-
-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.
-
-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.
 
 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. 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.
 
 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
-[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.
 ~~~~
+
+## 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.