# Prime Number JavaScript: Explained with Examples

In this article, we will discuss the prime number in JavaScript, understand how to define if a number is prime using JavaScript, and provide example codes to demonstrate the concepts.

Prime numbers are a necessary concept in mathematics and have multiple applications in different fields, including cryptography, number theory, and computer science.

In JavaScript, prime numbers are integers greater than 1 that are divisible only by 1 and themselves.

They play an essential role in many algorithms and applications.

## Understanding Prime Numbers

A prime number is a common number greater than 1 that has no positive divisors other than 1 and itself.

Furthermore, it cannot be evenly divided by any other number except for these two.

For example, 2, 3, 5, 7, 11, and 13 are prime numbers, as they have no divisors other than 1 and themselves.

On the other hand, 4, 6, 8, and 9 are not prime because they have divisors other than 1 and themselves.

## Checking for Prime Numbers in JavaScript

To determine whether a given number is prime or not in JavaScript, we can use a simple method that requires checking if the number is divisible by any integer between 2 and the square root of the number.

If the number is divisible by any of these integers, it is not prime. Otherwise, it is prime. This method is effective for reasonably sized numbers.

### Example Code of Checking Prime Numbers

``````function isPrimeSaple(numberValue) {
if (numberValue <= 1) {
return false;
}

if (numberValue <= 3) {
return true;
}

if (numberValue % 2 === 0 || numberValue % 3 === 0) {
return false;
}

for (let i = 5; i * i <= numberValue; i += 6) {
if (numberValue % i === 0 || numberValue % (i + 2) === 0) {
return false;
}
}

return true;
}

console.log(isPrimeSaple(2));
console.log(isPrimeSaple(9));
console.log(isPrimeSaple(17));
``````

Also read the other article in JavaScript: CreateTextNode JavaScript with Example Codes

### Example Code of Generating Prime Numbers

We can also set up a list of prime numbers within an expected range using the Sieve of Eratosthenes algorithm.

``````function generatePrimesInRange(start, end) {
let primes = [];
let isPrime = new Array(end + 1).fill(true);
isPrime[0] = false;
isPrime[1] = false;

for (let i = 2; i * i <= end; i++) {
if (isPrime[i]) {
for (let j = i * i; j <= end; j += i) {
isPrime[j] = false;
}
}
}

for (let i = Math.max(2, start); i <= end; i++) {
if (isPrime[i]) {
primes.push(i);
}
}

return primes;
}

// Generate prime numbers between 10 and 50
console.log(generatePrimesInRange(10, 50));  // [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
``````

Output:

``````[
11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97
]``````

## Conclusion

Prime numbers are fundamental mathematical entities with practical applications in different domains.

JavaScript provides genuine methods for checking whether a number is a prime and generating prime numbers within a given range.

The provided example codes that illustrate how to implement these functionalities effectively using JavaScript.

By understanding prime numbers and their properties, developers can improve their problem-solving skills and create more effective algorithms for different tasks.