# [Golang] Summation of Primes - Problem 10 - Project Euler

Go solution to summation of primes - Problem 10 - Project Euler. [1]

Problem:

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

Solution:

142913828922

We use sieve of Eratosthenes [2] to find out all prime number under 2,000,000. Note that we cannot use int type because of integer overflow [3]. Use int64 type instead.

Run Code on Go Playground

```package main

import (
"fmt"
)

func SieveOfEratosthenes(n int64) []int64 {
// 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 := int64(2); i < n+1; i++ {
integers[i] = true
}

for p := int64(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 []int64
for p := int64(2); p <= n; p++ {
if integers[p] == true {
primes = append(primes, p)
}
}

return primes
}

func main() {
primes := SieveOfEratosthenes(2000000)
fmt.Println(len(primes))
sum := int64(0)
for _, prime := range primes {
sum1 := sum + prime
if sum1 < sum {
fmt.Println(sum)
} else {
sum = sum1
}
}
fmt.Println(sum)
}
```

Tested on: Go Playground

References: