// 0007.go contains some functions to solve ProjectEuler.net's Problem #7
// https://projecteuler.net/problem=7
package main

import "fmt"

// IsPrimeNumber returns true if a given number is a prime number annd false
// if not. The given number is assumed to be a positive number.
func IsPrimeNumber(number int) bool {
	if number == 2 || number == 3 {
		// Return true as 2,3 are always prime
		return true
	}

	if number == 1 || number % 2 == 0 || number % 3 == 0 {
		// Return false as 1 or numbers dividable by 2,3 are never prime
		return false
	}

	// Loop to find other possible primes
	for i := 5; i*i <= number; i += 6 {
		if number % i == 0 || number % (i+2) == 0 {
			// Factor found, number cannot be prime
			return false
		}
	}

	// No factors were found, number must be prime
	return true
}

// NthPrime finds the nth prime number, given the number to find (n).
func NthPrime(n int) int {
	// Initialise variables
	count := 1
	i := 3

	for i = 3; count < n; i+=2 {
		if IsPrimeNumber(i) {
			// Check if number is prime
			count += 1
		}
	}

	// Backtrack one loop
	return i-2
}

func main(){
	// Answer the problem
	fmt.Println(NthPrime(10001))
}