56 lines
1.3 KiB
Markdown
56 lines
1.3 KiB
Markdown
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---
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title: 10001st prime
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localeTitle: 第10001个素数
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---
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## 问题7：10001个素数
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### 方法：
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* 素数是一个除以1和自身的数字。
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* 我们可以发现一个数字是素数，如果它不能被小于其自身的其他素数整除。
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### 解：
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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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\- [运行代码](https://repl.it/@ezioda004/Project-Euler-Problem-7-10001st-prime)
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### 参考文献：
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* [维基百科](https://en.wikipedia.org/wiki/Prime_number)
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