How to implement basic number theory algorithms (prime factorization, prime checking) in Go?

To implement basic number theory algorithms like prime factorization and prime checking in Go, you can use the following code snippets:

Prime Checking:

package main

import (
    "fmt"
    "math"
)

func isPrime(n int) bool {
    if n <= 1 {
        return false
    }
   
    for i := 2; i <= int(math.Sqrt(float64(n))); i++ {
        if n%i == 0 {
            return false
        }
    }
   
    return true
}

func main() {
    fmt.Println(isPrime(11)) // Output: true
    fmt.Println(isPrime(12)) // Output: false
}

Prime Factorization:

package main

import (
    "fmt"
)

func primeFactorization(n int) []int {
    factors := []int{}
    
    for i := 2; i <= n; i++ {
        for n%i == 0 {
            factors = append(factors, i)
            n /= i
        }
    }
    
    return factors
}

func main() {
    fmt.Println(primeFactorization(24)) // Output: [2 2 2 3]
    fmt.Println(primeFactorization(33)) // Output: [3 11]
}

You can run these snippets in a Go file (main.go) and execute them using the go run command in your terminal:

$ go run main.go