Check for Primeness of a Number in JavaScript

The thing about Prime Numbers

Prime numbers are tricky to spot.
A number that looks like a prime may in fact be a multiple of a smaller prime number.

So let's see how to know for sure that a number is a prime.
Of-course there is only one way:

Code in JavaScript for Checking Prime Numbers

A prime number is one that can only be divided by itself and one (1).

Consider the number 97.
To know for sure whether it is a prime number, we will recursively (repetitively) divide it by every number between 2 and 96 (97 minus 1).
If none of these divisors gives a remainder of zero, then 97 is certainly a prime number.

Create a new file; On Notepad++: File, New.
Call it CheckPrime.html.
Type out the adjoining JavaScript code for checking for primeness.

Base Theory of Quick-Check for Primeness in JavaScript

Since the world is always in a hurry, we can make use of a little extra speed.

Consider the number 36; Its factors are:

1, 2, 3, 4, 6, 9, 12, 18 and 36.

Every factor of 36, when arranged in ascending or descending order, can be divided into 2 equal parts at the position of its square-root.

1, 2, 3, 4, |, 9, 12, 18, 36

It is easily seen that every factor of 36 on one side of the divide has a complementary factor on the other side.

Hence, we can search for only a particular group of factors, (preferably the more compact group, i.e, between 1 and √36) to see if 36 has any factors.

Fast Check for Primeness in JavaScript

So for our quick check, we will use the range of 2 to √number.
Type out the adjoining JavaScript code for fast prime number check.

JavaScript code for CheckingPrime.html.

<!DOCTYPE html>
<html lang="en">
    <head>
        <meta charset="utf-8" />
        <title>Testing For A Prime Number</title>
    </head>
    <body>

        <h4>The number 97 seems like a prime number. Let's find out.</h4>
        <div id="test_result"></div>

        <script>
            var prime_suspect = 97; // We are suspecting this to be a prime number
            var failed_test = false; // We will change it to 'true' if 'prime_suspect' fails our test

            /* The easy way out is to loop numbers 2 - 96 and see if they can divide
            97 without without remainder. */
            for (var i = 2; i < prime_suspect; i++) {
                if ((prime_suspect % i) == 0) { // %(modulus) is explained below.
                    failed_test = true;
                    document.getElementById("test_result").innerHTML =
                    "No, " + prime_suspect + " is not a prime number. The number " + i + " is a factor of " + prime_suspect;
                    break; // Abandon the rest of the loop. 'prime_suspect' has failed our test.
                }
            }

            if (failed_test == false) { // see if prime_suspect passed the test
                document.getElementById("test_result").innerHTML = "Yes, " + prime_suspect + " is a prime number.";
            }
        </script>
    </body>
</html>

CheckPrimeFast.html

<!DOCTYPE html>
<html lang="en">
    <head>
        <meta charset="utf-8" />
        <title>Testing For A Prime Number</title>
    </head>
    <body>

        <h4>The number 91 seems like a prime number. Let's find out.</h4>
        <div id="test_result"></div>

        <script>
            var prime_suspect = 91; // We are suspecting this to be a prime number
            var test_range = Math.sqrt(prime_suspect); // square root
            test_range = Math.abs(test_range); // test_range may have come out as a decimal number, make it absolute.
            var failed_test = false; // We will change it to 'true' if 'prime_suspect' fails our test

            /* Check in the range 2 - √97 instead. */
            for (var i = 2; i <= test_range; i++) {
                if ((prime_suspect % i) == 0) { // modulus(%) is explained below.
                    failed_test = true;
                    document.getElementById("test_result").innerHTML =
                    "No, " + prime_suspect + " is not a prime number. The number " + i + " is a factor of " + prime_suspect;
                    break; // Abandon the rest of the loop. 'prime_suspect' has failed our test.
                }
            }

            if (failed_test == false) { // see if prime_suspect passed the test
                document.getElementById("test_result").innerHTML = "Yes, " + prime_suspect + " is a prime number.";
            }
        </script>
    </body>
</html>

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