Finding the nth prime number in JavaScript

In this article, we'll learn how to find the nth prime number using JavaScript. A prime number is a positive integer greater than 1 that has no divisors other than 1 and itself.

Understanding the Problem

We need to create a JavaScript function that takes an input n and returns the nth prime number. For example, if n=5, we should return 11 (the 5th prime number in the sequence: 2, 3, 5, 7, 11).

Algorithm Approach

We'll use a two-step approach:

1. Helper Function: Create an isPrime() function to check if a number is prime
2. Main Function: Use a counter to find the nth prime by testing consecutive numbers

Implementation

Step 1: Prime Number Checker

The isPrime() function checks divisibility from 2 up to the square root of the number:

function isPrime(num) {
    if (num <= 1) {
        return false;
    }
    for (let i = 2; i <= Math.sqrt(num); i++) {
        if (num % i === 0) {
            return false;
        }
    }
    return true;
}

// Test the function
console.log(isPrime(2));   // First prime
console.log(isPrime(17));  // Prime number
console.log(isPrime(15));  // Not prime

true
true
false

Step 2: Finding the nth Prime

function isPrime(num) {
    if (num <= 1) {
        return false;
    }
    for (let i = 2; i <= Math.sqrt(num); i++) {
        if (num % i === 0) {
            return false;
        }
    }
    return true;
}

function findNthPrime(n) {
    let count = 0;
    let num = 2;
    
    while (count < n) {
        if (isPrime(num)) {
            count++;
        }
        num++;
    }
    return num - 1;
}

// Examples
console.log("5th prime:", findNthPrime(5));
console.log("10th prime:", findNthPrime(10));
console.log("25th prime:", findNthPrime(25));

5th prime: 11
10th prime: 29
25th prime: 97

How It Works

1. isPrime(): Returns false for numbers ? 1, then checks divisibility from 2 to ?num
2. findNthPrime(): Starts from 2, counts prime numbers until reaching the nth prime
3. Counter Logic: Increments count when a prime is found, increments num each iteration
4. Return Value: Returns num - 1 because num is incremented after finding the nth prime

Complete Example with Multiple Tests

function isPrime(num) {
    if (num <= 1) return false;
    for (let i = 2; i <= Math.sqrt(num); i++) {
        if (num % i === 0) return false;
    }
    return true;
}

function findNthPrime(n) {
    let count = 0;
    let num = 2;
    while (count < n) {
        if (isPrime(num)) count++;
        num++;
    }
    return num - 1;
}

// Test with first 10 primes
console.log("First 10 primes:");
for (let i = 1; i <= 10; i++) {
    console.log(`${i}th prime: ${findNthPrime(i)}`);
}

First 10 primes:
1th prime: 2
2th prime: 3
3th prime: 5
4th prime: 7
5th prime: 11
6th prime: 13
7th prime: 17
8th prime: 19
9th prime: 23
10th prime: 29

Time and Space Complexity

• Time Complexity: O(n × ?m), where n is the position and m is the nth prime number
• Space Complexity: O(1), using only a few variables

Conclusion

This solution efficiently finds the nth prime number using a helper function to check primality and a main function to iterate through numbers. The algorithm is straightforward and works well for moderate values of n.