Check a Number is Prime or Not Using JavaScript (original) (raw)

Last Updated : 16 Apr, 2025

A prime number is a whole number greater than 1, which has no positive divisors other than 1 and itself. In other words, prime numbers cannot be formed by multiplying two smaller natural numbers. For example:

2, 3, 5, 7, 11, and 13 are prime numbers.
4, 6, 8, 9, and 12 are not prime numbers because they can be divided by numbers other than 1 and themselves.

Why Checking for Prime Numbers is Important

Prime numbers have applications in various fields, including:

Cryptography: Prime numbers play a significant role in encryption algorithms.
Algorithms and Data Structures: Prime numbers help in hashing functions, data security, and even in the distribution of resources.
Mathematics: Prime numbers are the building blocks of number theory, used in proofs and mathematical theorems.

Here are the different ways to check whether a number is Prime or not.

1. Iterative Check: Basic Approach

This is the simplest way to check for prime numbers by iterating through all numbers from 2 to n-1 and checking divisibility.

JavaScript ``

let n = 17; let isPrime = true;

if (n <= 1) { isPrime = false; } else { for (let i = 2; i < n; i++) { if (n % i === 0) { isPrime = false; break; } } }

console.log(isPrime ? ${n} is a prime number. : ${n} is not a prime number.);

It start by assuming the number n is prime (isPrime = true).
Use a loop to check divisibility from 2 to n-1. If any divisor is found, set isPrime to false.

2. Iterative Check: Optimized Approach

This method is more efficient because we only need to check for divisibility up to the square root of the number (sqrt(n)). This reduces unnecessary checks.

JavaScript ``

let n = 17; let isPrime = true;

if (n <= 1) { isPrime = false; } else { for (let i = 2; i * i <= n; i++) { if (n % i === 0) { isPrime = false; break; } } }

console.log(isPrime ? ${n} is a prime number. : ${n} is not a prime number.);

Reduce iterations by checking divisors only up to the square root of n.
This significantly improves performance for larger numbers.

3. Checking Multiple Numbers in an Array

If you want to check many numbers at once, this method loops through an array and stores the result for each number.

JavaScript `

Checks each number in the array one by one.
Stores the result in an object like {3: true, 4: false, 5: true, ...}.
Useful for bulk prime checks.

4. Using Sieve of Eratosthenes Algorithm

The Sieve of Eratosthenes is the most efficient way to check for prime numbers up to a maximum value by marking non-prime numbers in bulk.

JavaScript `

let max = 20; // Maximum number to check let a = new Array(max + 1).fill(true); a[0] = a[1] = false;

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

let obj = {}; for (let i = 0; i <= max; i++) { obj[i] = a[i]; }

console.log(obj);

Starts with an array where every number is marked as prime (true).
Then marks all multiples of each prime as not prime (false).
Fast and efficient for finding all primes up to a maximum number.

5. Bitwise Optimization Approach

This approach avoids checking even numbers beyond 2 and uses step increments to skip unnecessary iterations.

JavaScript ``

let n = 19; let isPrime = n > 1 && !(n % 2 === 0 && n !== 2);

for (let i = 3; i * i <= n && isPrime; i += 2) { if (n % i === 0) { isPrime = false; } }

console.log(isPrime ? ${n} is a prime number. : ${n} is not a prime number.);

Avoid even number checks beyond 2 for efficiency.
Use bitwise operations and step increment by 2 to skip even numbers.

6. Recursion-Based Prime Check

A recursive approach uses a recursive function that keeps checking for divisibility by increasing divisors until it reaches the square root of the number.

JavaScript ``

let n = 13; let isPrime = true;

function check(num, divisor = 2) { if (num <= 1) return false; if (divisor * divisor > num) return true; if (num % divisor === 0) return false; return check(num, divisor + 1); }

isPrime = check(n); console.log(isPrime ? ${n} is a prime number. : ${n} is not a prime number.);

Calls the same function again and again with the next divisor.
Stops when it finds a factor or reaches √n.
Clean and elegant for learning and small values.

Conclusion

To check if a number is prime, you can use different methods, such as checking divisibility up to the square root for efficiency or using the Sieve of Eratosthenes for multiple numbers. The optimized square root method is usually the best balance between simplicity and performance.