In this challenge, you are to list a set of prime numbers from 2 to x (where x can be any number). I have looked at a number of examples out there, most people use two loops (nested) to determine whether a number is divisible by any number within 1 to itself. So if you are to list all prime numbers up to 100. At 50, it checks to see if it can divide 50 by any number between 1-50. Same goes to 51, 52, 53, etc, until 100. It sounds logical but I really don’t like nested loop, and I avoid it at all cost. From my old math class, the first set of prime numbers are: 2, 3, 5, 7. So what if I print those numbers first, then I check if the next set of numbers are divisible into any of these numbers. You use these four numbers as your base. For example, 8 can be divided evenly by 2 and 4 so it’s not a prime, 9 can be divided evenly by 3 so it’s not a prime, 10 can be divided evenly by 2 and 5 so it’s not a prime, but 11 cannot be divided evenly by any of these four numbers so it’s a prime number. The logic (list) goes on and on. So to list ALL prime numbers up to 100, you can use the following code snippet:

<?php
$out = "2,3,5,7";
echo $out;
for ($x=8; $x<=100; $x++) {
    if ( ($x % 2 != 0) && ($x % 2 != 0) && ($x % 2 != 0) && ($x % 2 != 0) )
    echo ",".$x;
}
?>

After running this script, you will get the following numbers printed: 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