# Project Euler: #7 - 10001st prime

### **Problem**

By listing the first six prime numbers: `2, 3, 5, 7, 11, and 13`, we can see that the `6`th prime is `13`.

What is the `10001`st prime number?

---

### **Problem Description**

We all know about Prime Numbers. A number that is divisible by `1` and `itself` is called a **Prime Number**. In other words, it has only 2 factors - `1` and `itself`.

So we need to find the `nth` prime number. For example, `3rd` prime number is `5`, `4th` prime is `7`, `6th` prime is `13`, `10th` prime is `29` and so on.

We need to find the `10001`st prime number.

---

### **Approach**

To find `nth` prime number, we need to loop through a range of numbers from `2` to `Number.MAX_SAFE_INTEGER`.

Increase the counter by `1` for each prime number and once we find the `nth` prime, we break out of the loop.

To Check for the prime number, we use the same technique as in [Problem #3 Largest prime factor](https://theintrovertcoder.hashnode.dev/series/project-euler)

---

### **Solution**

```javascript
const isPrime = num => {
    if (num === 1) return false;
    if (num === 2 || num === 3) return true;
    if (num %2 === 0 || num % 3 === 0) return false;
            
    for (let i = 5; i <= Math.ceil(num / 2); i += 6) {
        if (num % i === 0 || num % (i+2) === 0) return false;
    }
    return true;
}

let count = 0;

for (let i = 2; i < Number.MAX_SAFE_INTEGER; i++) {
    if (isPrime(i)) count++;
    
    if (count === n) {
        console.log(i);
        break;
    }
}

console.time("10th");
console.log(nthPrime(10)); // 29
console.timeEnd("10th"); // 10th: 0.221923828125 ms

console.time("100th");
console.log(nthPrime(100)); // 541
console.timeEnd("100th"); // 100th: 0.68701171875 ms

console.time("10001th");
console.log(nthPrime(10001)); // 104743
console.timeEnd("10001th"); // 10001th: 827.61181640625 ms
```

You can find my solution on GitHub [**07**](https://github.com/sansk/project-euler-solutions-javascript/tree/main/07)

This particular solution was `timed out` in Hacker rank for 2 out of 7 test cases. So a little bit of tweaking is necessary to achieve a better time complexity.

If you have a better solution, please leave it in the comments below.

But no worries, the above code works perfectly fine for our use case, `10001th` prime number.

For the other Project Euler Solutions, please follow the series [**Project Euler Solutions in JS.**](https://theintrovertcoder.hashnode.dev/series/project-euler)

Thank you!