Listing Prime Numbers in JavaScript

Randomness of Prime Numbers

Prime numbers, in ascending order, are:

2, 3, 5, 7, 11, 13, 17, 19, 23, ...

Because prime numbers are so random in their progression, they are very difficult to predict as they get larger.

Hence writing a JavaScript code to list prime numbers will involve checking every number in a range of interest and gathering those that are without factors.

Say we want to list all prime numbers between 2 and 100 inclusive, we would start from 2; check to see whether it has any factors; keep it as a prime number if it has no factors; otherwise discard it.
We would then go to 3, and repeat the same process.
Repeat same for 4, 5, 6, 7, ..., 98, 99, 100.

Code that lists Prime Numbers in JavaScript

But we can always use a few tricks .

We will take the following steps:

Step 1:

First, we'll start our range from 9 (keeping 2, 3, 5, and 7 as prime numbers).

Step 2:

Next, we'll only check through odd numbers.

Step 3:

Next, we'll check against the factors 2, 3, and 5.

Step 4:

Lastly, we'll check with a subset of smaller prime numbers that we'll gather as our check progresses.

Create 2 new files; On Notepad++: File, New.
Call them PrimeNumbers.html and PrimeNumbers.js.
Type out the adjoining JavaScript code that lists prime numbers.

JavaScript code for PrimeNumbers.html

<!DOCTYPE html>

<html lang="en">
    <head>
        <meta charset="utf-8" />
        <title>Listing Prime Numbers</title>
        <script src="PrimeNumbers.js"></script>
    </head>
    <body>
        <h4>
            Prime numbers are numbers that can only be divided by themselves and 1
            without remainder.<br />Here is a list of them (between 1 and 99 inclusive).
        </h4>

        <div id="my_primes"></div>

        <script>
            /*
            * The array variable prime_numbers has our prime numbers.
            * Use the array method 'join' to display the values.
            */
            document.getElementById("my_primes").innerHTML = prime_numbers.join(", ");
        </script>
    </body>
</html>

PrimeNumbers.js

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