# Problem 7: 10001st prime

## Problem Explanation

• A prime number is a number which is divided by 1 and itself.
• We can find a number is prime if it’s not divisible by other prime numbers smaller than itself.

## Solutions

Solution 1 (Click to Show/Hide)
``````function nthPrime(n) {
//Primes array which will store all the prime numbers
const primes = [2];

//Num is the number we want to check
let num = 3,
isPrime = true;

//Looping until primes array is equal to n
while (primes.length < n) {
//All the primes numbers of a number is always <= its square root
let max = Math.ceil(Math.sqrt(num));

for (let i = 0; primes[i] <= max; i++) {
if (num % primes[i] == 0) {
//Looping till we find the prime
isPrime = false;
break;
}
}

//if Prime found, push it to the array
if (isPrime) primes.push(num);
isPrime = true;

//An optimization technique, since we know of all even numbers only 2 is a prime number, we can skip the rest
num += 2;
}

//Returning the last number
return primes[primes.length - 1];
}
``````

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