How to Check Prime Number in JavaScript

Introduction to Prime Numbers in JavaScript

A prime number is an integer larger than one that possesses only one and itself as its divisors. Therefore, if a prime number is divided by any integer lower than itself, it will never yield a whole number. A frequent exercise in programming is making a program test if a number is prime or not. This can be implemented on the client side using JavaScript and force the client computer to do the calculation. The following article is going to explain how to test if a number is prime or not using JavaScript.

Logic

We can check if a number is prime by dividing the number by all the integers from 1 up to one less than the number. If there is no remainder in any of these divisions, then the number is divisible and, therefore, not prime.

Let's take a look at some examples for better comprehension:

13 is only divisible by 1 and 13 itself; if we divide it by any other number, like 7, then the remainder will be 6. But 12 has the divisors 1, 2, 3, 4, and 6, so it is not a prime number. Here, we can observe that the smallest prime number is 2, and surprisingly, it is the only even prime number.

Here are the first 20 primes:

There are several ways to test if a number is prime, all referred to as primality tests.

Methods to Test Prime Numbers in JavaScript

Example 1: Using For Loop

The simplest way to check if a number (let's call it x) is a prime is to see if there are divisors (let's call them d) of x with 1 < d < x. Also, we are aware that for any number x, there can never be divisors d such that d > x/2. We will thus look for any number in the range [2, x/2] that will be a divisor of x. If we can obtain one, then we can say that x will not be a prime number, otherwise, it is.

Code

We called the function checkForPrime() when the value was input. We first verified whether the user had provided valid input. The input cannot be negative or empty since prime numbers cannot be negative.

We then used a flag to verify whether, while dividing the number by all the integers from 2 to n-1, we ever obtained a zero remainder.

If we ever obtained a zero, it indicates that the number is not prime, so we would reverse the flag's status, terminate the loop, and mark that number as not prime. If the flag's status never gets reversed, it indicates that we never obtained a zero remainder, and we can mark that number as prime.

Output

Example 2: Using While Loop

This example here is to showcase another way of implementation in JavaScript.

Code

Output

In the present case, a while loop is employed to test for divisibility of the number, restricting the tests to n/2. This approach is founded on a mathematical theorem that says that a number can never be evenly divisible by any integer higher than half of the number. By this approach, we increase efficiency by reducing the number of divisions required.

Example 3: Using Recursion

Code

Output

Here, a new function based on recursion has been defined. It has base cases in line with the intrinsic logic, making the function call itself until it reaches such base cases. The function will divide the number by each of the divisors from 2 to n-1 and yield a result depending on the remainder.

Conclusion

1. We have viewed the property number as prime and applied logic accordingly in JavaScript. We can apply different types of loops to achieve the same.
2. Prime numbers are those which can only be divided by 1 and by themselves with no remainder.
3. Prime numbers are discovered in JavaScript by iterating from numbers up to n and checking for divisors.