Step 1: Gathering Prime Number Candidates

We'll start by creating an array of integers up to n+1. Since prime numbers must be natural numbers greater than 1, we can discard 0 and 1.

Here's a visual representation of what we're doing:

Here's how we initialize our candidates in both JavaScript and Python:

1prime = [True] * (n + 1)

This provides us with all potential prime number candidates smaller than n.