# [Golang] 10001st Prime - Problem 7 - Project Euler

Go solution to 10001st prime - Problem 7 - Project Euler. [1]

**Problem**:

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

**Solution**:

According to prime number theorem, the 10001st prime number is probably located at somewhere around 1,000,000. We use Sieve of Eratosthenes [2] to find all prime numbers under 1,100,000. The number of primes is 10,453, and the 10001st prime is104743.

```
package main
import (
"fmt"
)
func SieveOfEratosthenes(n int) []int {
// Create a boolean array "prime[0..n]" and initialize
// all entries it as true. A value in prime[i] will
// finally be false if i is Not a prime, else true.
integers := make([]bool, n+1)
for i := 2; i < n+1; i++ {
integers[i] = true
}
for p := 2; p*p <= n; p++ {
// If integers[p] is not changed, then it is a prime
if integers[p] == true {
// Update all multiples of p
for i := p * 2; i <= n; i += p {
integers[i] = false
}
}
}
// return all prime numbers <= n
var primes []int
for p := 2; p <= n; p++ {
if integers[p] == true {
primes = append(primes, p)
}
}
return primes
}
func main() {
primes := SieveOfEratosthenes(110000)
fmt.Println(len(primes))
if len(primes) > 10001 {
fmt.Println(primes[10000])
}
}
```

Tested on: Go Playground

References:

[1] | 10001st prime - Problem 7 - Project Euler |

[2] | [Golang] Sieve of Eratosthenes |