nthprime.go

package main

import "fmt"
import "os"
import "strconv"
import "math"

func sieve(n int) []int {

	isprime := make([]bool, n+1)

	for i := range isprime { // help. how do i initialize the array as all true
		isprime[i] = true
	}

	isprime[0] = false
	if len(isprime) > 1 {
		isprime[1] = false
	}

	max := int(math.Ceil(math.Sqrt(float64(n))))

	for i := 2; i <= max; i++ {
		if isprime[i] == true {
			for j := i * i; j <= n; j += i {
				isprime[j] = false
			}
		}
	}

	var primes []int

	for i, v := range isprime {
		if v == true {
			primes = append(primes, i)
		}
	}
	return primes
}

func main() {
	nthprime, err := strconv.Atoi(os.Args[1] - 1)
	if err != nil {
		fmt.Println(err)
	}

	var searchbound int
	var searchmultiplier float64

	if nthprime == 1 {
		searchbound = 2
	} else {

		if nthprime < 11 {
			searchmultiplier = 3
		} else {
			searchmultiplier = 1.2408246135107 // found this via trial and error
		}
		searchbound = int(math.Log(float64(nthprime)) * float64(nthprime) * searchmultiplier)
	}
	primes := sieve(searchbound)

	// efficiency := float64(nthprime) / float64(len(primes))
	// fmt.Printf("searched up to %d and found %d primes (efficiency of %.4f). prime number %d is:\n", searchbound, len(primes), efficiency, nthprime)

	fmt.Println(primes[nthprime])

}