primes.sh

#!/usr/bin/env bash

isPrime(){
    if [[ $1 -eq 2 ]] || [[ $1 -eq 3 ]]; then
        echo true
        return 0
    elif [[ $(($1 % 2)) -eq 0 ]] || [[ $(($1 % 3)) -eq 0 ]]; then
        echo false
        return 0
    fi
    i=5
    w=2
    while [[ $((i * i)) -le $1 ]]; do
        if [[ $(($1 % i)) -eq 0 ]]; then
            echo false
            return 0
        fi
        i=$((i + w))
        w=$((6 - w))
    done
    echo true
}

primeFactors() {
    local lastPrime=2
    local number="$1"
    if "$(isPrime "$number")"; then
        echo "($number)"
        return 0
    fi
    local result=""
    local counter=0
    while (( number % lastPrime == 0)); do
        number=$((number / lastPrime))
        counter=$((counter + 1))
    done
    if [[ $counter -eq 1 ]]; then
        result="${result}($lastPrime)"
    elif [[ $counter -ne 0 ]]; then
        result="${result}($lastPrime**$counter)"
    fi
    lastPrime=3
    counter=0
    while (( number % lastPrime == 0)); do
        number=$((number / lastPrime))
        counter=$((counter + 1))
    done
    if [[ $counter -eq 1 ]]; then
        result="${result}($lastPrime)"
    elif [[ $counter -ne 0 ]]; then
        result="${result}($lastPrime**$counter)"
    fi
    while (( number > 1 )); do
        lastPrime=$((lastPrime + 2))
        while ! $(isPrime $lastPrime); do
            lastPrime=$((lastPrime + 2))
        done
        counter=0
        while (( number % lastPrime == 0 )); do
            number=$((number / lastPrime))
            counter=$((counter + 1))
        done
        if [[ $counter -eq 1 ]]; then
            result="${result}($lastPrime)"
        elif [[ $counter -ne 0 ]]; then
            result="${result}($lastPrime**$counter)"
        fi
        if $(isPrime "$number"); then
            result="${result}($number)"
            number=1
        fi
    done
    echo "$result"
}

primeFactors $1