50 lines
1.2 KiB
Markdown
50 lines
1.2 KiB
Markdown
---
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title: 10001st prime
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---
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## Problem 7: 10001st prime
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### Method:
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- A prime number is a number which is divided by 1 and itself.
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- We can find a number is prime if it's not divisible by other prime numbers smaller than itself.
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### Solution:
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```js
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function nthPrime(n) {
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//Primes array which will store all the prime numbers
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const primes = [2];
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//Num is the number we want to check
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let num = 3, isPrime = true;
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//Looping until primes array is equal to n
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while (primes.length < n){
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//All the primes numbers of a number is always <= it's square root
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let max = Math.ceil(Math.sqrt(num));
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for (let i = 0; primes[i] <= max; i++){
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if (num % primes[i] == 0) {
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//Looping till we find the prime
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isPrime = false;
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break;
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}
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}
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//if Prime found, push it to the array
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if (isPrime) primes.push(num);
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isPrime = true;
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//An optimization technique, since we know of all even numbers only 2 is a prime number, we can skip the rest
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num+=2;
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}
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//Returning the last number
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return primes[primes.length-1];
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}
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```
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-[Run Code](https://repl.it/@ezioda004/Project-Euler-Problem-7-10001st-prime)
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### References:
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- [Wikipedia](https://en.wikipedia.org/wiki/Prime_number)
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