Here's the algorithm in plain words: Let's create the list of primes up to $n. We start with just 2 as the known prime. Then, for each number $i between 3 and $n, we do the following: we try to divide the number $i by all the known primes up to sqrt $i. If any of them divides the number, then it can't be prime. If none of them divides it, it is a prime, though: because a) if a non-prime $d divides $i, then $d = $p1 * $d1, where $p1 is prime, and $p1 divides $i; b) if a number $p2 greater than sqrt $i divides $i, then $i / $p2 must be less than sqrt $i, and it must divide $i. If we find a new prime, we push it to the list.

• I don't eliminate numbers ending with 2, 4, 5, 6, 8, and 0, because they get eliminated in the 0 == $i % $p test.
• testing every number for sqrt $i == int sqrt $i wouldn't help us much, as it happens rarely.
• the @primes loop, as described above, tries to divide the candidate $i by all the known primes up to sqrt $i, to check its primality.
• $n represents the highest number, we are interested in primes less or equal $n. $i is the candidate, i.e. the number we might include in the @primes list if it passes the primality test. $p is a known prime less or equal sqrt $i.

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